A characterisation of the ellipsoid in terms of concurrent sections.
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G.R. Burton, P. Mani (1978)
Commentarii mathematici Helvetici
V. Caselles, A. Chambolle, S. Moll, M. Novaga (2008)
Annales de l'I.H.P. Analyse non linéaire
H. Martini (1990)
Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry
Elisabeth Werner (1999)
Studia Mathematica
Let K be a convex body in and B be the Euclidean unit ball in . We show that , where as(K) respectively as(B) is the affine surface area of K respectively B and , are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].
P.M. Gruber (1995)
Discrete & computational geometry
Donara Nguon (1993)
Bulletin de la Société Mathématique de France
F. Aurenhammer (1990)
Discrete & computational geometry
Ling, Joseph M. (2007)
Beiträge zur Algebra und Geometrie
Kharazishvili, A. (2002)
Georgian Mathematical Journal
Martin Kružík (2003)
Mathematica Bohemica
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
Siniša Vrećica (1981)
Publications de l'Institut Mathématique
Hüsseinov, F. (1999)
Journal of Convex Analysis
Zhang, Gaoyong (1999)
Annals of Mathematics. Second Series
L. Low (1976)
Acta Arithmetica
R.R. Hall (1992)
Journal für die reine und angewandte Mathematik
A. Figalli, F. Maggi, A. Pratelli (2009)
Annales de l'I.H.P. Analyse non linéaire
J.R. Sangwine-Yager (1994)
Mathematische Annalen
Gilbert Crombez (2006)
Czechoslovak Mathematical Journal
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
Stephen S.-T. Yau, Yi-Jing Xu (1995)
Journal für die reine und angewandte Mathematik
T. Figiel (1976)
Compositio Mathematica
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