Results 31 to 40 of about 13,857 (195)
A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces
, 2010 In this paper we give a lower bound on the waist of the unit sphere of a uniformly convex normed space by using the localization technique in codimension greater than one and a strong version of the Borsuk-Ulam theorem.
Alesker +5 more
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Notices of the American Mathematical SocietyComment: to appear in Notices Amer.
Eichmair, Michael, Brendle, Simon
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Exact Face-isoperimetric Inequalities
European Journal of Combinatorics, 1990 Let \([p]^ N\) be the grid, i.e. \([p]^ N=\{0,1,...,N-1\}\). The authors give the best possible upper bound for the number of faces of a fixed dimension contained in a subset of the grid. As a conjecture the result appeared in \textit{B. Bollobás} and \textit{A. J. Radcliffe} [Eur. J. Comb. 11, No.4, 323-333 (1990; see the review above)].
Bollobás, Béla, Leader, Imre
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Analytic isoperimetric inequalities [PDF]
Mathematical Inequalities & Applications, 2000 It is known that the classical geometric isoperimetric inequalities are equivalent to suitable analytic isoperimetric inequalities. For example, the analytic isoperimetric inequality \[ \left( \sum_{i=1}^{n}\sin \theta _{i}\right) ^{2}\geq d_{n}(\sigma)\sum_{i=1}^{n}\sin \theta _{i}\cos \theta _{i}+ \left(n\sin \sigma -\sum_{i=1}^{n}\sin \theta _{i ...
Ku, Hsu-Tung, Ku, Mei-Chin
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Lp Affine Isoperimetric Inequalities [PDF]
Journal of Differential Geometry, 2000 An affine isoperimetric inequality compares two functionals associated with convex (or more general) bodies, where the ratio of the functionals is invariant under non-degenerate linear transformations. The article deals with affine isoperimetric inequalities for centroid and projection bodies. The most important inequality concerning centroid bodies is
Lutwak, Erwin +2 more
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On Isoperimetric Inequalities in Minkowski Spaces
Journal of Inequalities and Applications, 2010 The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Horst Martini, Zokhrab Mustafaev
doaj +2 more sources
Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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Isoperimetric problems for a nonlocal perimeter of Minkowski type
, 2017 We prove a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under convexity constraints.
Cesaroni, Annalisa, Novaga, Matteo
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Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality
Journal of Function Spaces, 2020 The first variation of the total mass of log-concave functions was studied by Colesanti and Fragalà, which includes the Lp mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-
Niufa Fang, Jin Yang
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley +1 more source