Ludwig, Monika Geometric valuation theory. (English) Zbl 1528.52008 Hujdurović, Ademir (ed.) et al., European congress of mathematics. Proceedings of the 8th congress, 8ECM, Portorož, Slovenia, June 20–26, 2021. Berlin: European Mathematical Society (EMS). 93-123 (2023). Reviewer: Peter McMullen (London) MSC: 52B45 46E35 52A20 26B25 PDFBibTeX XMLCite \textit{M. Ludwig}, in: European congress of mathematics. Proceedings of the 8th congress, 8ECM, Portorož, Slovenia, June 20--26, 2021. Berlin: European Mathematical Society (EMS). 93--123 (2023; Zbl 1528.52008) Full Text: DOI arXiv
Tatarko, Kateryna; Werner, Elisabeth M. \(L_p\)-Steiner quermassintegrals. (English) Zbl 1526.52008 Adv. Math. 430, Article ID 109205, 35 p. (2023). Reviewer: Boris Rubin (Baton Rouge) MSC: 52A39 28A75 52A20 53A07 PDFBibTeX XMLCite \textit{K. Tatarko} and \textit{E. M. Werner}, Adv. Math. 430, Article ID 109205, 35 p. (2023; Zbl 1526.52008) Full Text: DOI arXiv
Hepworth, Richard Groups of convex bodies. (English) Zbl 1522.52004 Geom. Dedicata 217, No. 4, Paper No. 76, 17 p. (2023). Reviewer: Peter McMullen (London) MSC: 52A20 28A75 52B45 19D99 PDFBibTeX XMLCite \textit{R. Hepworth}, Geom. Dedicata 217, No. 4, Paper No. 76, 17 p. (2023; Zbl 1522.52004) Full Text: DOI arXiv
Colesanti, Andrea; Ludwig, Monika; Mussnig, Fabian The Hadwiger theorem on convex functions. IV: The Klain approach. (English) Zbl 1510.26008 Adv. Math. 413, Article ID 108832, 35 p. (2023). Reviewer: Rolf Schneider (Freiburg im Breisgau) MSC: 26B25 49Q20 52A41 52A39 52B45 PDFBibTeX XMLCite \textit{A. Colesanti} et al., Adv. Math. 413, Article ID 108832, 35 p. (2023; Zbl 1510.26008) Full Text: DOI arXiv
Wannerer, Thomas Classification of angular curvature measures and a proof of the angularity conjecture. (English) Zbl 1503.53141 Am. J. Math. 144, No. 5, 1331-1366 (2022). Reviewer: Fernando Etayo Gordejuela (Santander) MSC: 53C65 53C20 58J60 52B45 52A20 PDFBibTeX XMLCite \textit{T. Wannerer}, Am. J. Math. 144, No. 5, 1331--1366 (2022; Zbl 1503.53141) Full Text: DOI arXiv
Alesker, Semyon Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies. (English) Zbl 1497.52011 Isr. J. Math. 247, No. 1, 361-378 (2022). Reviewer: Robert Dawson (Halifax) MSC: 52A40 52A39 52B45 PDFBibTeX XMLCite \textit{S. Alesker}, Isr. J. Math. 247, No. 1, 361--378 (2022; Zbl 1497.52011) Full Text: DOI arXiv
Dong, W. Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions. (English) Zbl 1485.80002 Proc. Natl. Acad. Sci. USA 118, No. 3, Paper No. e2019873118, 6 p. (2021). MSC: 80A10 82C24 PDFBibTeX XMLCite \textit{W. Dong}, Proc. Natl. Acad. Sci. USA 118, No. 3, Paper No. e2019873118, 6 p. (2021; Zbl 1485.80002) Full Text: DOI
Grygierek, Jens Multivariate normal approximation for functionals of random polytopes. (English) Zbl 1465.52018 J. Theor. Probab. 34, No. 2, 897-922 (2021). MSC: 52A22 60D05 60F05 52B05 PDFBibTeX XMLCite \textit{J. Grygierek}, J. Theor. Probab. 34, No. 2, 897--922 (2021; Zbl 1465.52018) Full Text: DOI arXiv
Faifman, Dmitry; Wannerer, Thomas The Weyl principle on the Finsler frontier. (English) Zbl 1462.53013 Sel. Math., New Ser. 27, No. 2, Paper No. 27, 30 p. (2021). MSC: 53B40 52B45 52A39 PDFBibTeX XMLCite \textit{D. Faifman} and \textit{T. Wannerer}, Sel. Math., New Ser. 27, No. 2, Paper No. 27, 30 p. (2021; Zbl 1462.53013) Full Text: DOI arXiv
Li, Jin SL\((n)\) covariant function-valued valuations. (English) Zbl 1458.52005 Adv. Math. 377, Article ID 107462, 41 p. (2021). Reviewer: Fabian Mußnig (Firenze) MSC: 52B45 52A20 52B11 44A10 PDFBibTeX XMLCite \textit{J. Li}, Adv. Math. 377, Article ID 107462, 41 p. (2021; Zbl 1458.52005) Full Text: DOI arXiv
Xu, Wenxue Integral geometric inequalities and valuations. (English) Zbl 1433.52005 Geom. Dedicata 204, 365-375 (2020). Reviewer: Florian Pausinger (Belfast) MSC: 52A22 52A20 PDFBibTeX XMLCite \textit{W. Xu}, Geom. Dedicata 204, 365--375 (2020; Zbl 1433.52005) Full Text: DOI
Vitale, R. A. On an exponential functional for Gaussian processes and its geometric foundations. (English. Russian original) Zbl 1415.60038 J. Math. Sci., New York 238, No. 4, 406-414 (2019); translation from Zap. Nauchn. Semin. POMI 457, 101-113 (2017). MSC: 60G15 60D05 60E15 PDFBibTeX XMLCite \textit{R. A. Vitale}, J. Math. Sci., New York 238, No. 4, 406--414 (2019; Zbl 1415.60038); translation from Zap. Nauchn. Semin. POMI 457, 101--113 (2017) Full Text: DOI
Böröczky, Károly J.; Ludwig, Monika Minkowski valuations on lattice polytopes. (English) Zbl 1506.52016 J. Eur. Math. Soc. (JEMS) 21, No. 1, 163-197 (2019). Reviewer: Matthias Schymura (Cottbus) MSC: 52B20 52B45 PDFBibTeX XMLCite \textit{K. J. Böröczky} and \textit{M. Ludwig}, J. Eur. Math. Soc. (JEMS) 21, No. 1, 163--197 (2019; Zbl 1506.52016) Full Text: DOI arXiv
Colesanti, Andrea; Lombardi, Nico; Parapatits, Lukas Translation invariant valuations on quasi-concave functions. (English) Zbl 1471.26005 Stud. Math. 243, No. 1, 79-99 (2018). Reviewer: Mohammad W. Alomari (Irbid) MSC: 26B25 52A41 52B45 PDFBibTeX XMLCite \textit{A. Colesanti} et al., Stud. Math. 243, No. 1, 79--99 (2018; Zbl 1471.26005) Full Text: DOI arXiv
Bernig, Andreas Valuations and curvature measures on complex spaces. (English) Zbl 1373.53103 Vedel Jensen, Eva B. (ed.) et al., Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014. Cham: Springer (ISBN 978-3-319-51950-0/pbk; 978-3-319-51951-7/ebook). Lecture Notes in Mathematics 2177, 235-260 (2017). Reviewer: V. V. Chueshev (Kemerovo) MSC: 53C65 53C55 PDFBibTeX XMLCite \textit{A. Bernig}, Lect. Notes Math. 2177, 235--260 (2017; Zbl 1373.53103) Full Text: DOI arXiv
Schuster, Franz E. A Hadwiger-type theorem for general tensor valuations. (English) Zbl 1372.52008 Vedel Jensen, Eva B. (ed.) et al., Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014. Cham: Springer (ISBN 978-3-319-51950-0/pbk; 978-3-319-51951-7/ebook). Lecture Notes in Mathematics 2177, 157-183 (2017). MSC: 52A20 53C65 PDFBibTeX XMLCite \textit{F. E. Schuster}, Lect. Notes Math. 2177, 157--183 (2017; Zbl 1372.52008) Full Text: DOI
Alesker, Semyon Structures on valuations. (English) Zbl 1372.52018 Vedel Jensen, Eva B. (ed.) et al., Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014. Cham: Springer (ISBN 978-3-319-51950-0/pbk; 978-3-319-51951-7/ebook). Lecture Notes in Mathematics 2177, 67-78 (2017). Reviewer: Rolf Schneider (Freiburg i. Br.) MSC: 52B45 53C65 PDFBibTeX XMLCite \textit{S. Alesker}, Lect. Notes Math. 2177, 67--78 (2017; Zbl 1372.52018) Full Text: DOI
Schneider, Rolf Valuations on convex bodies: the classical basic facts. (English) Zbl 1369.52020 Vedel Jensen, Eva B. (ed.) et al., Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014. Cham: Springer (ISBN 978-3-319-51950-0/pbk; 978-3-319-51951-7/ebook). Lecture Notes in Mathematics 2177, 1-25 (2017). MSC: 52B45 PDFBibTeX XMLCite \textit{R. Schneider}, Lect. Notes Math. 2177, 1--25 (2017; Zbl 1369.52020) Full Text: DOI
Colesanti, Andrea; Lombardi, Nico Valuations on the space of quasi-concave functions. (English) Zbl 1375.52010 Klartag, Bo’az (ed.) et al., Geometric aspects of functional analysis. Israel seminar (GAFA) 2014–2016. Cham: Springer (ISBN 978-3-319-45281-4/pbk; 978-3-319-45282-1/ebook). Lecture Notes in Mathematics 2169, 71-105 (2017). Reviewer: Sorin-Mihai Grad (Chemnitz) MSC: 52A41 52B45 26B25 PDFBibTeX XMLCite \textit{A. Colesanti} and \textit{N. Lombardi}, Lect. Notes Math. 2169, 71--105 (2017; Zbl 1375.52010) Full Text: DOI arXiv
Li, Jin; Ma, Dan Laplace transforms and valuations. (English) Zbl 1353.44001 J. Funct. Anal. 272, No. 2, 738-758 (2017). MSC: 44A10 52A20 52B45 PDFBibTeX XMLCite \textit{J. Li} and \textit{D. Ma}, J. Funct. Anal. 272, No. 2, 738--758 (2017; Zbl 1353.44001) Full Text: DOI arXiv
Bernig, Andreas; Voide, Floriane Spin-invariant valuations on the octonionic plane. (English) Zbl 1347.53065 Isr. J. Math. 214, No. 2, 831-855 (2016). MSC: 53C65 15A66 PDFBibTeX XMLCite \textit{A. Bernig} and \textit{F. Voide}, Isr. J. Math. 214, No. 2, 831--855 (2016; Zbl 1347.53065) Full Text: DOI arXiv
Hartley, David Stability of near cylindrical stationary solutions to weighted-volume preserving curvature flows. (English) Zbl 1344.53045 J. Geom. Anal. 26, No. 3, 2169-2203 (2016). MSC: 53C44 35K55 35B35 PDFBibTeX XMLCite \textit{D. Hartley}, J. Geom. Anal. 26, No. 3, 2169--2203 (2016; Zbl 1344.53045) Full Text: DOI arXiv
Kusejko, Katharina; Parapatits, Lukas A valuation-theoretic approach to translative-equidecomposability. (English) Zbl 1346.52005 Adv. Math. 297, 174-195 (2016). Reviewer: Christian Richter (Jena) MSC: 52B45 52A20 PDFBibTeX XMLCite \textit{K. Kusejko} and \textit{L. Parapatits}, Adv. Math. 297, 174--195 (2016; Zbl 1346.52005) Full Text: DOI arXiv
Cavallina, L.; Colesanti, A. Monotone valuations on the space of convex functions. (English) Zbl 1321.26027 Anal. Geom. Metr. Spaces 3, 167-211 (2015). MSC: 26B25 52A41 52B45 PDFBibTeX XMLCite \textit{L. Cavallina} and \textit{A. Colesanti}, Anal. Geom. Metr. Spaces 3, 167--211 (2015; Zbl 1321.26027) Full Text: DOI arXiv
Hug, Daniel; Schneider, Rolf Local tensor valuations. (English) Zbl 1366.52004 Geom. Funct. Anal. 24, No. 5, 1516-1564 (2014). MSC: 52A20 52A22 52A39 52B45 PDFBibTeX XMLCite \textit{D. Hug} and \textit{R. Schneider}, Geom. Funct. Anal. 24, No. 5, 1516--1564 (2014; Zbl 1366.52004) Full Text: DOI arXiv
Hyman, Jeffrey D.; Winter, C. Larrabee Stochastic generation of explicit pore structures by thresholding Gaussian random fields. (English) Zbl 1349.76817 J. Comput. Phys. 277, 16-31 (2014). MSC: 76S05 76F65 PDFBibTeX XMLCite \textit{J. D. Hyman} and \textit{C. L. Winter}, J. Comput. Phys. 277, 16--31 (2014; Zbl 1349.76817) Full Text: DOI
Alesker, Semyon On extendability by continuity of valuations on convex polytopes. (English) Zbl 1291.52019 Adv. Math. 255, 352-380 (2014). Reviewer: Christian Richter (Jena) MSC: 52B45 52A15 52A20 PDFBibTeX XMLCite \textit{S. Alesker}, Adv. Math. 255, 352--380 (2014; Zbl 1291.52019) Full Text: DOI arXiv
Baryshnikov, Y.; Ghrist, R.; Wright, M. Hadwiger’s theorem for definable functions. (English) Zbl 1286.52006 Adv. Math. 245, 573-586 (2013). MSC: 52B45 26B35 28A75 PDFBibTeX XMLCite \textit{Y. Baryshnikov} et al., Adv. Math. 245, 573--586 (2013; Zbl 1286.52006) Full Text: DOI arXiv
Schneider, Rolf Local tensor valuations on convex polytopes. (English) Zbl 1282.52008 Monatsh. Math. 171, No. 3-4, 459-479 (2013). Reviewer: Gabriela Cristescu (Arad) MSC: 52A20 52B45 PDFBibTeX XMLCite \textit{R. Schneider}, Monatsh. Math. 171, No. 3--4, 459--479 (2013; Zbl 1282.52008) Full Text: DOI
Parapatits, Lukas; Wannerer, Thomas On the inverse Klain map. (English) Zbl 1280.52003 Duke Math. J. 162, No. 11, 1895-1922 (2013). Reviewer: Peter McMullen (London) MSC: 52A20 52B45 52A40 PDFBibTeX XMLCite \textit{L. Parapatits} and \textit{T. Wannerer}, Duke Math. J. 162, No. 11, 1895--1922 (2013; Zbl 1280.52003) Full Text: DOI arXiv Euclid
Abardia, Judit Difference bodies in complex vector spaces. (English) Zbl 1262.52012 J. Funct. Anal. 263, No. 11, 3588-3603 (2012). Reviewer: Christian Richter (Jena) MSC: 52B45 52A20 52A39 PDFBibTeX XMLCite \textit{J. Abardia}, J. Funct. Anal. 263, No. 11, 3588--3603 (2012; Zbl 1262.52012) Full Text: DOI arXiv
Leinster, Tom Integral geometry for the 1-norm. (English) Zbl 1252.53088 Adv. Appl. Math. 49, No. 2, 81-96 (2012). Reviewer: Erhard Heil (Darmstadt) MSC: 53C65 52A01 52A21 52A30 51F99 PDFBibTeX XMLCite \textit{T. Leinster}, Adv. Appl. Math. 49, No. 2, 81--96 (2012; Zbl 1252.53088) Full Text: DOI arXiv
Parapatits, Lukas; Schuster, Franz E. The Steiner formula for Minkowski valuations. (English) Zbl 1252.52011 Adv. Math. 230, No. 3, 978-994 (2012). Reviewer: Paolo Dulio (Milano) MSC: 52B45 52A40 PDFBibTeX XMLCite \textit{L. Parapatits} and \textit{F. E. Schuster}, Adv. Math. 230, No. 3, 978--994 (2012; Zbl 1252.52011) Full Text: DOI arXiv
Bernig, Andreas Integral geometry under \(G_2\) and \(Spin(7)\). (English) Zbl 1262.53067 Isr. J. Math. 184, 301-316 (2011). Reviewer: Valery Vladimirovich Volchkov (Donetsk) MSC: 53C65 53C30 PDFBibTeX XMLCite \textit{A. Bernig}, Isr. J. Math. 184, 301--316 (2011; Zbl 1262.53067) Full Text: DOI arXiv
Milman, Vitali D.; Schneider, Rolf Characterizing the mixed volume. (English) Zbl 1242.52011 Adv. Geom. 11, No. 4, 669-689 (2011). Reviewer: Markus Kiderlen (Aarhus) MSC: 52A39 PDFBibTeX XMLCite \textit{V. D. Milman} and \textit{R. Schneider}, Adv. Geom. 11, No. 4, 669--689 (2011; Zbl 1242.52011) Full Text: DOI
Alesker, Semyon A Fourier-type transform on translation-invariant valuations on convex sets. (English) Zbl 1219.52009 Isr. J. Math. 181, 189-294 (2011); corrigendum ibid. 200, 507-508 (2014). Reviewer: Serge Lawrencenko (Moskva) MSC: 52B45 42B10 53C65 52A22 52A39 PDFBibTeX XMLCite \textit{S. Alesker}, Isr. J. Math. 181, 189--294 (2011; Zbl 1219.52009) Full Text: DOI arXiv
Heveling, Matthias; Reitzner, Matthias Poisson-Voronoi approximation. (English) Zbl 1172.60003 Ann. Appl. Probab. 19, No. 2, 719-736 (2009). Reviewer: Viktor Oganyan (Erevan) MSC: 60D05 60G55 52A22 60C05 PDFBibTeX XMLCite \textit{M. Heveling} and \textit{M. Reitzner}, Ann. Appl. Probab. 19, No. 2, 719--736 (2009; Zbl 1172.60003) Full Text: DOI arXiv
McMullen, Peter Valuations on lattice polytopes. (English) Zbl 1161.52010 Adv. Math. 220, No. 1, 303-323 (2009). Reviewer: Matthias Beck (San Francisco) MSC: 52B20 52B45 PDFBibTeX XMLCite \textit{P. McMullen}, Adv. Math. 220, No. 1, 303--323 (2009; Zbl 1161.52010) Full Text: DOI
Vitale, R. A. On the Gaussian representation of intrinsic volumes. (English) Zbl 1145.60022 Stat. Probab. Lett. 78, No. 10, 1246-1249 (2008). MSC: 60G15 52A07 52A22 52A39 60D05 60E15 PDFBibTeX XMLCite \textit{R. A. Vitale}, Stat. Probab. Lett. 78, No. 10, 1246--1249 (2008; Zbl 1145.60022) Full Text: DOI
Hug, D.; Schneider, R.; Schuster, R. The space of isometry covariant tensor valuations. (English) Zbl 1134.52008 St. Petersbg. Math. J. 19, No. 1, 137-158 (2008) and Algebra Anal. 19, No. 1, 194-224 (2007). Reviewer: Peter McMullen (London) (MR2319515) MSC: 52A39 52A38 52B45 PDFBibTeX XMLCite \textit{D. Hug} et al., St. Petersbg. Math. J. 19, No. 1, 137--158 (2008; Zbl 1134.52008) Full Text: DOI
Ludwig, Monika Minkowski valuations. (English) Zbl 1077.52005 Trans. Am. Math. Soc. 357, No. 10, 4191-4213 (2005). Reviewer: Rolf Schneider (Freiburg i. Br.) MSC: 52A20 52B11 52B45 PDFBibTeX XMLCite \textit{M. Ludwig}, Trans. Am. Math. Soc. 357, No. 10, 4191--4213 (2005; Zbl 1077.52005) Full Text: DOI
Alesker, Semyon; Bernstein, Joseph Range characterization of the cosine transform on higher Grassmannians. (English) Zbl 1059.22013 Adv. Math. 184, No. 2, 367-379 (2004). Reviewer: Markus Stroppel (Stuttgart) MSC: 22E45 22E50 43A85 53C35 14M15 PDFBibTeX XMLCite \textit{S. Alesker} and \textit{J. Bernstein}, Adv. Math. 184, No. 2, 367--379 (2004; Zbl 1059.22013) Full Text: DOI arXiv
Ludwig, Monika Projection bodies and valuations. (English) Zbl 1019.52003 Adv. Math. 172, No. 2, 158-168 (2002). Reviewer: Rolf Schneider (Freiburg i.Br.) MSC: 52A20 52B45 PDFBibTeX XMLCite \textit{M. Ludwig}, Adv. Math. 172, No. 2, 158--168 (2002; Zbl 1019.52003) Full Text: DOI
Ludwig, Monika Valuations on polytopes containing the origin in their interiors. (English) Zbl 1015.52012 Adv. Math. 170, No. 2, 239-256 (2002). Reviewer: Rolf Schneider (Freiburg i.Br.) MSC: 52B45 52A20 PDFBibTeX XMLCite \textit{M. Ludwig}, Adv. Math. 170, No. 2, 239--256 (2002; Zbl 1015.52012) Full Text: DOI Link
Alesker, S. On P. McMullen’s conjecture on translation invariant valuations. (English) Zbl 0971.52004 Adv. Math. 155, No. 2, 239-263 (2000). Reviewer: Rolf Schneider (Freiburg i.Br.) MSC: 52A20 52B45 52A39 PDFBibTeX XMLCite \textit{S. Alesker}, Adv. Math. 155, No. 2, 239--263 (2000; Zbl 0971.52004) Full Text: DOI
Klain, Daniel A. Even valuations on convex bodies. (English) Zbl 0940.52002 Trans. Am. Math. Soc. 352, No. 1, 71-93 (2000). Reviewer: R.Schneider (Freiburg i.Br.) MSC: 52A20 52B45 52A22 52A38 52A39 PDFBibTeX XMLCite \textit{D. A. Klain}, Trans. Am. Math. Soc. 352, No. 1, 71--93 (2000; Zbl 0940.52002) Full Text: DOI
Ludwig, Monika; Reitzner, Matthias A characterization of affine surface area. (English) Zbl 0947.52003 Adv. Math. 147, No. 1, 138-172 (1999). Reviewer: K.Leichtweiß (Stuttgart) MSC: 52A20 53A15 PDFBibTeX XMLCite \textit{M. Ludwig} and \textit{M. Reitzner}, Adv. Math. 147, No. 1, 138--172 (1999; Zbl 0947.52003) Full Text: DOI Link
Klain, Daniel A. An Euler relation for valuations on polytopes. (English) Zbl 0944.52007 Adv. Math. 147, No. 1, 1-34 (1999). Reviewer: Serguey M.Pokas (Odessa) MSC: 52B45 PDFBibTeX XMLCite \textit{D. A. Klain}, Adv. Math. 147, No. 1, 1--34 (1999; Zbl 0944.52007) Full Text: DOI Link
Klain, Daniel A. Kinematic formulas for finite vector spaces. (English) Zbl 0893.52005 Discrete Math. 179, No. 1-3, 121-132 (1998). Reviewer: M.Lassak (Bydgoszcz) MSC: 52A35 52A38 PDFBibTeX XMLCite \textit{D. A. Klain}, Discrete Math. 179, No. 1--3, 121--132 (1998; Zbl 0893.52005) Full Text: DOI
Klain, Daniel A. Kinematic formulas for finite lattices. (English) Zbl 0926.05003 Ann. Comb. 1, No. 4, 353-366 (1997). MSC: 05A19 52A22 05A05 05A10 PDFBibTeX XMLCite \textit{D. A. Klain}, Ann. Comb. 1, No. 4, 353--366 (1997; Zbl 0926.05003) Full Text: DOI