Results 1 to 10 of about 707 (41)
Stability of volume comparison for complex convex bodies [PDF]
, 2011 We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex ...
Koldobsky, Alexander
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From $r$-dual sets to uniform contractions [PDF]
, 2017 Let $M^d$ denote the $d$-dimensional Euclidean, hyperbolic, or spherical space. The $r$-dual set of given set in $M^d$ is the intersection of balls of radii $r$ centered at the points of the given set.
Bezdek, Karoly
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Equivariant absolute extensor property on hyperspaces of convex sets [PDF]
, 2014 Let G be a compact group acting on a Banach space L by means of linear isometries. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact convex subsets of L endowed with the Hausdorff metric topology.
Jonard-Pérez, Natalia
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A bound for the perimeter of inner parallel bodies [PDF]
, 2016 We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that |∂Ω_t| ≥ (1−t/r)^(n−1)₊|∂Ω|.
Larson, Simon
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, 2016 We show that for any two convex curves $C_1$ and $C_2$ in $\mathbb R^d$ parametrized by $[0,1]$ with opposite orientations, there exists a hyperplane $H$ with the following property: For any $t\in [0,1]$ the points $C_1(t)$ and $C_2(t)$ are never in the ...
Holmsen, Andreas F. +2 more
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H\"older continuity for support measures of convex bodies
, 2015 The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous.
Hug, Daniel, Schneider, Rolf
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Tverberg-type theorems for intersecting by rays
, 2010 In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point ...
A. Hatcher +21 more
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On the X-ray number of almost smooth convex bodies and of convex bodies of constant width
, 2009 The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width
Bezdek, Gy. Kiss, K. Bezdek, Tóth
core +2 more sources
Affine invariant valuations on polytopes
, 2016 A classification of SL$(n)$ invariant valuations on the space of convex polytopes in $R^n$ without any continuity assumptions is established.
Ludwig, Monika, Reitzner, Matthias
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On variational problems related to steepest descent curves and self dual convex sets on the sphere
, 2014 Let $\mathcal{C}$ be the family of compact convex subsets $S$ of the hemisphere in $\rn$ with the property that $S$ contains its dual $S^*;$ let $u\in S^*$, and let $ \Phi(S,u)=\frac{2}{\omega_n}\int_{S}\ \,\, d\sigma(\theta).
Longinetti, Marco +2 more
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