50 years sets with positive reach -- a survey.
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Thäle, C. (2008)
Surveys in Mathematics and its Applications
Meyer, Mathieu, Reisner, Shlomo (2000)
Beiträge zur Algebra und Geometrie
Rolf Schneider (1990)
Manuscripta mathematica
Alexander I. Bobenko, Ivan Izmestiev (2008)
Annales de l’institut Fourier
We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized convex...
Böröczky, Károly jun. (1996)
Mathematica Pannonica
Stepanov, V.N. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Lin, Si, Bin, Xiong, Wuyang, Yu (2006)
Journal of Inequalities and Applications [electronic only]
Vadlamani, Sreekar, Adler, Robert J. (2006)
Electronic Communications in Probability [electronic only]
Yuan, Jun, Leng, Gangsong (2006)
Journal of Inequalities and Applications [electronic only]
Ulrich Betke, Martin Henk (1993)
Monatshefte für Mathematik
Károly, Jr. Böröczky (1994)
Monatshefte für Mathematik
M. Henk, M.Á. Hernández-Cifre (2008)
Revista Matemática Iberoamericana
Eugenia Saorín (2009)
Banach Center Publications
We consider the problem of classifying the convex bodies in the 3-dimensional space depending on the differentiability of their associated quermassintegrals with respect to the one-parameter-depending family given by the inner/outer parallel bodies. It turns out that this problem is closely related to some behavior of the roots of the 3-dimensional Steiner polynomial.
Fenghong, Lu, Weihong, Mao, Gangsong, Leng (2007)
Journal of Inequalities and Applications [electronic only]
Randolf Arnold (1993)
Monatshefte für Mathematik
Schneider, Rolf (1993)
Beiträge zur Algebra und Geometrie
Kampf, Jürgen (2009)
Beiträge zur Algebra und Geometrie
Richard J. Gardner, Daniel Hug, Wolfgang Weil (2013)
Journal of the European Mathematical Society
An investigation is launched into the fundamental characteristics of operations on and between sets, with a focus on compact convex sets and star sets (compact sets star-shaped with respect to the origin) in -dimensional Euclidean space . It is proved that if , with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, covariant, and associative if and only if it is addition for some . It is also demonstrated that if ,...
Andrea Colesanti, Carlo Pucci (1997)
Forum mathematicum
P. Filliman (1992)
Monatshefte für Mathematik
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