Edit Profile (opens in new tab) Rataj, Jan Co-Author Distance Author ID: rataj.jan Published as: Rataj, Jan; Rataj, J. Homepage: https://www2.karlin.mff.cuni.cz/~rataj/index_en.html External Links: MGP · ORCID · Wikidata · ResearchGate · dblp · GND · IdRef Documents Indexed: 61 Publications since 1985, including 2 Books and 1 Additional arXiv Preprint Reviewing Activity: 15 Reviews Co-Authors: 26 Co-Authors with 42 Joint Publications 506 Co-Co-Authors all top 5 Co-Authors 19 single-authored 9 Zähle, Martina 5 Zajíček, Luděk 4 Hug, Daniel 4 Saxl, Ivan 4 Winter, Steffen 3 Pokorný, Dušan 3 Weil, Wolfgang 2 Beneš, Viktor 2 Kiderlen, Markus 2 Lešanovský, Antonín 2 Mrkvička, Tomáš 2 Spodarev, Evgueni 2 Vedel Jensen, Eva Bjørn 1 Auneau, Jérémy 1 Fu, Joseph Howland Guthrie 1 Goodey, Paul R. 1 Hinderer, Wolfram 1 Hojek, Stanislav 1 Honzl, Ondřej 1 Krejčír, Pavel 1 Meschenmoser, Daniel 1 Ohser, Joachim 1 Pelikán, Karol 1 Preiss, David 1 Schmidt, Volker 1 Zitek, Frantisek all top 5 Serials 8 Mathematische Nachrichten 5 Geometriae Dedicata 3 Advances in Applied Probability 3 Časopis Pro Pěstování Matematiky 3 Czechoslovak Mathematical Journal 3 Mathematika 2 Journal of Mathematical Analysis and Applications 2 Beiträge zur Algebra und Geometrie 2 Advances in Mathematics 2 Indiana University Mathematics Journal 2 Annals of Global Analysis and Geometry 2 Statistics 2 Mathematica Bohemica 2 Stochastic Processes and their Applications 2 Advances in Geometry 1 Houston Journal of Mathematics 1 Journal of Applied Probability 1 Kybernetika 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 Advances in Applied Mathematics 1 The Annals of Applied Probability 1 Differential Geometry and its Applications 1 The Journal of Geometric Analysis 1 Applications of Mathematics 1 Journal of Fractal Geometry 1 Springer Monographs in Mathematics all top 5 Fields 31 Differential geometry (53-XX) 31 Probability theory and stochastic processes (60-XX) 30 Convex and discrete geometry (52-XX) 15 Measure and integration (28-XX) 8 Statistics (62-XX) 5 Real functions (26-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Number theory (11-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 47 Publications have been cited 322 times in 182 Documents Cited by ▼ Year ▼ Curvatures and currents for unions of sets with positive reach. II. Zbl 0997.53062 Rataj, J.; Zähle, M. 28 2001 On volume and surface area of parallel sets. Zbl 1234.28008 Rataj, Jan; Winter, Steffen 23 2010 Normal cycles of Lipschitz manifolds by approximation with parallel sets. Zbl 1042.53053 Rataj, J.; Zähle, M. 18 2003 Characterization of Minkowski measurability in terms of surface area. Zbl 1273.28003 Rataj, Jan; Winter, Steffen 18 2013 Stochastic geometry: Selected topics. Zbl 1052.60001 Beneš, Viktor; Rataj, Jan 17 2004 On the structure of sets with positive reach. Zbl 1375.26026 Rataj, Jan; Zajíček, Luděk 17 2017 General normal cycles and Lipschitz manifolds of bounded curvature. Zbl 1146.53309 Rataj, J.; Zähle, M. 16 2005 On infinitesimal increase of volumes of morphological transforms. Zbl 1117.28002 Kiderlen, Markus; Rataj, Jan 15 2006 On the expected surface area of the Wiener sausage. Zbl 1166.60049 Rataj, Jan; Schmidt, Volker; Spodarev, Evgeny 13 2009 Normal cycles and curvature measures of sets with d.c. boundary. Zbl 1286.58002 Pokorný, Dušan; Rataj, Jan 11 2013 Mixed curvature measures for sets of positive reach and a translative integral formula. Zbl 0844.53050 Rataj, J.; Zähle, M. 9 1995 Translative and kinematic formulae for curvature measures of flat sections. Zbl 0944.53044 Rataj, Jan 9 1999 Kinematic formulas for sets defined by differences of convex functions. Zbl 1403.53062 Fu, Joseph H. G.; Pokorný, Dušan; Rataj, Jan 9 2017 Curvature measures of singular sets. Zbl 1423.28001 Rataj, Jan; Zähle, Martina 9 2019 Determination of spherical area measures by means of dilation volumes. Zbl 1005.52004 Rataj, Jan 8 2002 On the estimation of intrinsic volume densities of stationary random closed sets. Zbl 1148.62023 Mrkvička, T.; Rataj, J. 7 2008 Curvature densities of self-similar sets. Zbl 1279.28016 Rataj, Jan; Zähle, Martina 7 2012 A rotational integral formula for intrinsic volumes. Zbl 1154.60010 Jensen, Eva B. Vedel; Rataj, Jan 6 2008 A flag representation of projection functions. Zbl 1401.52008 Goodey, Paul; Hinderer, Wolfram; Hug, Daniel; Rataj, Jan; Weil, Wolfgang 5 2017 On estimation of the Euler number by projections of thin slabs. Zbl 1070.60010 Rataj, J. 5 2004 A product integral representation of mixed volumes of two convex bodies. Zbl 1284.52006 Hug, Daniel; Rataj, Jan; Weil, Wolfgang 5 2013 On boundaries of unions of sets with positive reach. Zbl 1097.53050 Rataj, J. 4 2005 Estimation of intrinsic volumes from parallel neighbourhoods. Zbl 1101.62084 Rataj, Jan 4 2006 Analysis of planar anisotropy by means of the Steiner compact. Zbl 0694.60010 Rataj, Jan; Saxl, Ivan 4 1989 The iterated version of a translative integral formula for sets of positive reach. Zbl 0902.53049 Rataj, Jan 4 1997 Estimation of oriented direction distribution of a planar body. Zbl 0861.60023 Rataj, Jan 4 1996 Almost sure asymptotic behaviour of the \(r\)-neighbourhood surface area of Brownian paths. Zbl 1249.28003 Honzl, Ondřej; Rataj, Jan 4 2012 Mixed curvature measures of translative integral geometry. Zbl 1397.53088 Hug, Daniel; Rataj, Jan 4 2018 On the structure of WDC sets. Zbl 1429.26022 Pokorný, Dušan; Rataj, Jan; Zajíček, Luděk 4 2019 Closed form of the rotational Crofton formula. Zbl 1235.60010 Auneau, Jérémy; Rataj, Jan; Jensen, Eva B. Vedel 3 2012 A translative integral formula for absolute curvature measures. Zbl 0985.53035 Rataj, Jan 3 2001 On set covariance and three-point test sets. Zbl 1049.52004 Rataj, J. 3 2004 Absolute curvature measures for unions of sets with positive reach. Zbl 1101.28004 Rataj, Jan 3 2002 Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces. Zbl 1260.53121 Rataj, Jan; Zajíček, Luděk 3 2012 A remark on mixed curvature measures for sets with positive reach. Zbl 1008.53060 Rataj, J.; Zähle, M. 3 2002 Approximations of the Wiener sausage and its curvature measures. Zbl 1205.60146 Rataj, Jan; Spodarev, Evgeny; Meschenmoser, Daniel 3 2009 Convergence of total variation of curvature measures. Zbl 1136.53054 Rataj, J. 2 2008 Flag representations of mixed volumes and mixed functionals of convex bodies. Zbl 1383.52007 Hug, Daniel; Rataj, Jan; Weil, Wolfgang 2 2018 Determination of compact sets in Euclidean spaces by the volume of their dilation. Zbl 0784.60018 Lešanovský, Antonín; Rataj, Jan 2 1990 Maximal sets of orthogonal measures are not analytic. Zbl 0631.28001 Preiss, David; Rataj, Jan 1 1985 Random paths in non-convex bodies. Zbl 0685.60014 Saxl, I.; Rataj, J. 1 1989 Characterization of compact sets by their dilation volume. Zbl 0826.60009 Rataj, Jan 1 1995 0-1 sequences having the same numbers of (1-1)-couples of given distances. Zbl 0762.11008 Lešanovský, Antonín; Rataj, Jan; Hojek, Stanislav 1 1992 Remarks on translative formula for sets of positive reach. Zbl 0868.53053 Rataj, Jan 1 1997 Random sets of finite perimeter. Zbl 1366.60014 Rataj, Jan 1 2015 Mean Lipschitz-Killing curvatures for homogeneous random fractals. Zbl 07754858 Rataj, Jan; Winter, Steffen; Zähle, Martina 1 2023 Dilation volumes of sets of finite perimeter. Zbl 1440.60012 Kiderlen, Markus; Rataj, Jan 1 2018 Mean Lipschitz-Killing curvatures for homogeneous random fractals. Zbl 07754858 Rataj, Jan; Winter, Steffen; Zähle, Martina 1 2023 Curvature measures of singular sets. Zbl 1423.28001 Rataj, Jan; Zähle, Martina 9 2019 On the structure of WDC sets. Zbl 1429.26022 Pokorný, Dušan; Rataj, Jan; Zajíček, Luděk 4 2019 Mixed curvature measures of translative integral geometry. Zbl 1397.53088 Hug, Daniel; Rataj, Jan 4 2018 Flag representations of mixed volumes and mixed functionals of convex bodies. Zbl 1383.52007 Hug, Daniel; Rataj, Jan; Weil, Wolfgang 2 2018 Dilation volumes of sets of finite perimeter. Zbl 1440.60012 Kiderlen, Markus; Rataj, Jan 1 2018 On the structure of sets with positive reach. Zbl 1375.26026 Rataj, Jan; Zajíček, Luděk 17 2017 Kinematic formulas for sets defined by differences of convex functions. Zbl 1403.53062 Fu, Joseph H. G.; Pokorný, Dušan; Rataj, Jan 9 2017 A flag representation of projection functions. Zbl 1401.52008 Goodey, Paul; Hinderer, Wolfram; Hug, Daniel; Rataj, Jan; Weil, Wolfgang 5 2017 Random sets of finite perimeter. Zbl 1366.60014 Rataj, Jan 1 2015 Characterization of Minkowski measurability in terms of surface area. Zbl 1273.28003 Rataj, Jan; Winter, Steffen 18 2013 Normal cycles and curvature measures of sets with d.c. boundary. Zbl 1286.58002 Pokorný, Dušan; Rataj, Jan 11 2013 A product integral representation of mixed volumes of two convex bodies. Zbl 1284.52006 Hug, Daniel; Rataj, Jan; Weil, Wolfgang 5 2013 Curvature densities of self-similar sets. Zbl 1279.28016 Rataj, Jan; Zähle, Martina 7 2012 Almost sure asymptotic behaviour of the \(r\)-neighbourhood surface area of Brownian paths. Zbl 1249.28003 Honzl, Ondřej; Rataj, Jan 4 2012 Closed form of the rotational Crofton formula. Zbl 1235.60010 Auneau, Jérémy; Rataj, Jan; Jensen, Eva B. Vedel 3 2012 Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces. Zbl 1260.53121 Rataj, Jan; Zajíček, Luděk 3 2012 On volume and surface area of parallel sets. Zbl 1234.28008 Rataj, Jan; Winter, Steffen 23 2010 On the expected surface area of the Wiener sausage. Zbl 1166.60049 Rataj, Jan; Schmidt, Volker; Spodarev, Evgeny 13 2009 Approximations of the Wiener sausage and its curvature measures. Zbl 1205.60146 Rataj, Jan; Spodarev, Evgeny; Meschenmoser, Daniel 3 2009 On the estimation of intrinsic volume densities of stationary random closed sets. Zbl 1148.62023 Mrkvička, T.; Rataj, J. 7 2008 A rotational integral formula for intrinsic volumes. Zbl 1154.60010 Jensen, Eva B. Vedel; Rataj, Jan 6 2008 Convergence of total variation of curvature measures. Zbl 1136.53054 Rataj, J. 2 2008 On infinitesimal increase of volumes of morphological transforms. Zbl 1117.28002 Kiderlen, Markus; Rataj, Jan 15 2006 Estimation of intrinsic volumes from parallel neighbourhoods. Zbl 1101.62084 Rataj, Jan 4 2006 General normal cycles and Lipschitz manifolds of bounded curvature. Zbl 1146.53309 Rataj, J.; Zähle, M. 16 2005 On boundaries of unions of sets with positive reach. Zbl 1097.53050 Rataj, J. 4 2005 Stochastic geometry: Selected topics. Zbl 1052.60001 Beneš, Viktor; Rataj, Jan 17 2004 On estimation of the Euler number by projections of thin slabs. Zbl 1070.60010 Rataj, J. 5 2004 On set covariance and three-point test sets. Zbl 1049.52004 Rataj, J. 3 2004 Normal cycles of Lipschitz manifolds by approximation with parallel sets. Zbl 1042.53053 Rataj, J.; Zähle, M. 18 2003 Determination of spherical area measures by means of dilation volumes. Zbl 1005.52004 Rataj, Jan 8 2002 Absolute curvature measures for unions of sets with positive reach. Zbl 1101.28004 Rataj, Jan 3 2002 A remark on mixed curvature measures for sets with positive reach. Zbl 1008.53060 Rataj, J.; Zähle, M. 3 2002 Curvatures and currents for unions of sets with positive reach. II. Zbl 0997.53062 Rataj, J.; Zähle, M. 28 2001 A translative integral formula for absolute curvature measures. Zbl 0985.53035 Rataj, Jan 3 2001 Translative and kinematic formulae for curvature measures of flat sections. Zbl 0944.53044 Rataj, Jan 9 1999 The iterated version of a translative integral formula for sets of positive reach. Zbl 0902.53049 Rataj, Jan 4 1997 Remarks on translative formula for sets of positive reach. Zbl 0868.53053 Rataj, Jan 1 1997 Estimation of oriented direction distribution of a planar body. Zbl 0861.60023 Rataj, Jan 4 1996 Mixed curvature measures for sets of positive reach and a translative integral formula. Zbl 0844.53050 Rataj, J.; Zähle, M. 9 1995 Characterization of compact sets by their dilation volume. Zbl 0826.60009 Rataj, Jan 1 1995 0-1 sequences having the same numbers of (1-1)-couples of given distances. Zbl 0762.11008 Lešanovský, Antonín; Rataj, Jan; Hojek, Stanislav 1 1992 Determination of compact sets in Euclidean spaces by the volume of their dilation. Zbl 0784.60018 Lešanovský, Antonín; Rataj, Jan 2 1990 Analysis of planar anisotropy by means of the Steiner compact. Zbl 0694.60010 Rataj, Jan; Saxl, Ivan 4 1989 Random paths in non-convex bodies. Zbl 0685.60014 Saxl, I.; Rataj, J. 1 1989 Maximal sets of orthogonal measures are not analytic. Zbl 0631.28001 Preiss, David; Rataj, Jan 1 1985 all cited Publications top 5 cited Publications all top 5 Cited by 183 Authors 28 Rataj, Jan 17 Hug, Daniel 10 Villa, Elena 10 Winter, Steffen 9 Svane, Anne Marie 9 Weil, Wolfgang 8 Kiderlen, Markus 8 Lapidus, Michel L. 8 Zähle, Martina 6 Pokorný, Dušan 6 Vedel Jensen, Eva Bjørn 5 Spodarev, Evgueni 4 Beneš, Viktor 4 Camerlenghi, Federico 4 Kampf, Jürgen 4 Kombrink, Sabrina 4 Last, Günter 4 Radunović, Goran 4 Staněk, Jakub 4 Staňková Helisová, Kateřina 4 Žubrinić, Darko 3 Capasso, Vincenzo 3 Fu, Joseph Howland Guthrie 3 Honzl, Ondřej 3 Longinetti, Marco 3 Lytchak, Alexander 3 Manselli, Paolo 3 Mecke, Klaus R. 3 Micheletti, Alessandra 3 Molchanov, Ilya S. 3 Mrkvička, Tomáš 3 Pogodaev, Nikolaĭ Il’ich 3 Santilli, Mario 3 Schneider, Rolf G. 3 Venturi, Adriana 2 Ambrosio, Luigi 2 Auneau, Jérémy 2 Ballani, Felix 2 Bernig, Andreas 2 Delfour, Michel Claude 2 Faifman, Dmitry 2 Fraiman, Ricardo 2 Glaunès, Joan Alexis 2 Hörrmann, Julia 2 Kapovitch, Vitali 2 Kesseböhmer, Marc 2 Khmaladze, Estate V. 2 Klatt, Michael Andreas 2 Lachièze-Rey, Raphaël 2 Morale, Daniela 2 Pawlas, Zbyněk 2 Pearse, Erin Peter James 2 Roussillon, Pierre 2 Saracco, Giorgio 2 Schmidt, Volker 2 Schulte, Matthias 2 Šedivý, Ondřej 2 Wannerer, Thomas 2 Weis, Jan A. 2 Yukich, Joseph Elliott 2 Zajíček, Luděk 1 Abardia-Evéquoz, Judit 1 Adams, Henry 1 Alessi, Alessio A. 1 Alonso-Ruiz, Patricia 1 Angiuli, Luciana 1 Baudoin, Fabrice 1 Berezhkovskii, Alexander M. 1 Bezrukov, Sergey M. 1 Bohl, Tilman Johannes 1 Böhlke, Thomas 1 Breidenbach, B. 1 Campi, Stefano 1 Černý, Rostislav 1 Chambolle, Antonin 1 Chazal, Frédéric 1 Chen, Li 1 Cholaquidis, Alejandro 1 Cibotaru, Daniel Florentiu 1 Cockreham, James 1 Cohen-Steiner, David 1 Colesanti, Andrea 1 Crasta, Graziano 1 Crouzet, Jean-François 1 Cruz-Orive, Luis Manuel 1 Cuevas, Antonio 1 Czarnecki, Marc-Olivier 1 Dann, Susanna 1 Dare, Emil 1 Del Nin, Giacomo 1 Deniz, Ali 1 Dereudre, David 1 Dettmers, Kristin 1 Dorogovtsev, Andriĭ Anatoliĭovych 1 Edalat, Abbas 1 Eichinger, Tobias 1 Ernesti, Felix 1 Fang, Yangqin 1 Fischer, Vera 1 Fradelizi, Matthieu ...and 83 more Authors all top 5 Cited in 78 Serials 11 Advances in Mathematics 10 Mathematische Nachrichten 10 Advances in Applied Mathematics 9 Advances in Applied Probability 6 Methodology and Computing in Applied Probability 5 Journal of Mathematical Analysis and Applications 5 Mathematika 5 Stochastic Processes and their Applications 5 Journal of Mathematical Imaging and Vision 4 Czechoslovak Mathematical Journal 3 Annals of the Institute of Statistical Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Geometriae Dedicata 3 Kybernetika 3 Annals of Global Analysis and Geometry 3 Discrete & Computational Geometry 3 The Annals of Applied Probability 3 Bernoulli 3 Journal of Fractal Geometry 2 Scandinavian Journal of Statistics 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Zeitschrift 2 SIAM Journal on Control and Optimization 2 Differential Geometry and its Applications 2 The Journal of Geometric Analysis 2 Calculus of Variations and Partial Differential Equations 2 Journal of Convex Analysis 2 Discrete and Continuous Dynamical Systems. Series S 1 Applicable Analysis 1 Israel Journal of Mathematics 1 Mathematical Biosciences 1 Mathematical Methods in the Applied Sciences 1 Metrika 1 Ukrainian Mathematical Journal 1 Chaos, Solitons and Fractals 1 American Journal of Mathematics 1 Fundamenta Mathematicae 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Journal of Geometry 1 Journal of Multivariate Analysis 1 Journal of Optimization Theory and Applications 1 Journal of Statistical Planning and Inference 1 Manuscripta Mathematica 1 Le Matematiche 1 Mathematische Annalen 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Statistics & Probability Letters 1 Statistics 1 Constructive Approximation 1 Applications of Mathematics 1 Geometric and Functional Analysis. GAFA 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 NoDEA. Nonlinear Differential Equations and Applications 1 Selecta Mathematica. New Series 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Geometry & Topology 1 Chaos 1 New Journal of Physics 1 Differential Equations 1 Advances in Geometry 1 Bulletin of the Brazilian Mathematical Society. New Series 1 GAMM-Mitteilungen 1 Electronic Journal of Statistics 1 SIAM Journal on Imaging Sciences 1 Set-Valued and Variational Analysis 1 Bulletin of Mathematical Sciences 1 Journal of Mathematics in Industry 1 Analysis and Geometry in Metric Spaces 1 Philosophical Transactions A. Royal Society of London 1 Actes des Rencontres du C.I.R.M. 1 Annales Fennici Mathematici all top 5 Cited in 36 Fields 75 Probability theory and stochastic processes (60-XX) 57 Convex and discrete geometry (52-XX) 56 Differential geometry (53-XX) 52 Measure and integration (28-XX) 36 Statistics (62-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 10 Number theory (11-XX) 10 Numerical analysis (65-XX) 9 Partial differential equations (35-XX) 8 Real functions (26-XX) 8 Computer science (68-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Information and communication theory, circuits (94-XX) 3 Mathematical logic and foundations (03-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Manifolds and cell complexes (57-XX) 3 Mechanics of deformable solids (74-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Geometry (51-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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