Caffarelli, L. A.; Oliker, V. I. Weak solutions of one inverse problem in geometric optics. (English. Russian original) Zbl 1202.78003 J. Math. Sci., New York 154, No. 1, 39-49 (2008); translation from Probl. Mat. Anal. 37, 37-46 (2008). MSC: 78A05 49N45 PDFBibTeX XMLCite \textit{L. A. Caffarelli} and \textit{V. I. Oliker}, J. Math. Sci., New York 154, No. 1, 39--49 (2008; Zbl 1202.78003); translation from Probl. Mat. Anal. 37, 37--46 (2008) Full Text: DOI
Oliker, Vladimir On the geometry of convex reflectors. II: Polar reflectors. (English) Zbl 1159.49031 Result. Math. 52, No. 3-4, 359-367 (2008). MSC: 49K20 35J60 78A05 PDFBibTeX XMLCite \textit{V. Oliker}, Result. Math. 52, No. 3--4, 359--367 (2008; Zbl 1159.49031) Full Text: DOI
Oliker, Vladimir I. A Minkowski-style theorem for focal functions of compact convex reflectors. (English) Zbl 1124.49016 Trans. Am. Math. Soc. 360, No. 2, 563-574 (2008). MSC: 49K20 35J65 78A05 PDFBibTeX XMLCite \textit{V. I. Oliker}, Trans. Am. Math. Soc. 360, No. 2, 563--574 (2008; Zbl 1124.49016) Full Text: DOI arXiv
Oliker, Vladimir Embedding \(\mathbb S^n\) into \(\mathbb R^{n+1}\) with given integral Gauss curvature and optimal mass transport on \(\mathbb S^n\). (English) Zbl 1233.49024 Adv. Math. 213, No. 2, 600-620 (2007). MSC: 49Q20 49J45 52C07 53C42 PDFBibTeX XMLCite \textit{V. Oliker}, Adv. Math. 213, No. 2, 600--620 (2007; Zbl 1233.49024) Full Text: DOI arXiv
Gangbo, Wilfrid; Oliker, Vladimir Existence of optimal maps in the reflector-type problems. (English) Zbl 1136.49015 ESAIM, Control Optim. Calc. Var. 13, No. 1, 93-106 (2007). MSC: 49J55 49J20 35J65 PDFBibTeX XMLCite \textit{W. Gangbo} and \textit{V. Oliker}, ESAIM, Control Optim. Calc. Var. 13, No. 1, 93--106 (2007; Zbl 1136.49015) Full Text: DOI arXiv Numdam EuDML
Oliker, Vladimir A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature. (English) Zbl 1089.53048 Opozda, Barbara (ed.) et al., PDEs, submanifolds and affine differential geometry. Proceedings of the conference and autumn school, Bȩdlewo, Poland, September 23–27, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 69, 81-90 (2005). Reviewer: I. G. Nikolaev (Urbana) MSC: 53C45 49K20 35J65 PDFBibTeX XMLCite \textit{V. Oliker}, Banach Cent. Publ. 69, 81--90 (2005; Zbl 1089.53048)
Glimm, Tilmann; Oliker, Vladimir Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle. (English) Zbl 1129.49309 Indiana Univ. Math. J. 53, No. 5, 1255-1277 (2004). MSC: 49Q20 35A15 35Q15 35Q60 78A05 90C48 PDFBibTeX XMLCite \textit{T. Glimm} and \textit{V. Oliker}, Indiana Univ. Math. J. 53, No. 5, 1255--1277 (2004; Zbl 1129.49309) Full Text: DOI arXiv
Glimm, Tilmann; Oliker, Vladimir Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem. (English. Russian original) Zbl 1049.49030 J. Math. Sci., New York 117, No. 3, 4096-4108 (2003); translation from Probl. Mat. Anal. 26, 47-66 (2003). Reviewer: V. Grebenev (Novosibirsk) MSC: 49Q20 49K20 35J65 78A05 90C05 PDFBibTeX XMLCite \textit{T. Glimm} and \textit{V. Oliker}, Probl. Mat. Anal. 26, 47--66 (2003; Zbl 1049.49030); translation from Probl. Mat. Anal. 26, 47--66 (2003)
Oliker, V. I. The problem of embedding \(S^ n\) into \(R^{n+1}\) with prescribed Gauss curvature and its solution by variational methods. (English) Zbl 0589.49028 Trans. Am. Math. Soc. 295, 291-303 (1986). Reviewer: H.Reckziegel MSC: 49Q20 53C42 53C45 PDFBibTeX XMLCite \textit{V. I. Oliker}, Trans. Am. Math. Soc. 295, 291--303 (1986; Zbl 0589.49028) Full Text: DOI