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pro vyhledávání: '"Hoehner, Steven"'
The aim of this paper is to introduce a generalization of Steiner symmetrization in Euclidean space for spherical space, which is the dual of the Steiner symmetrization in hyperbolic space introduced by Peyerimhoff (J. London Math. Soc. (2) 66: 753-7
Externí odkaz:
http://arxiv.org/abs/2406.10614
Autor:
Hoehner, Steven, Roysdon, Michael
A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) an
Externí odkaz:
http://arxiv.org/abs/2401.01033
Autor:
Hoehner, Steven, Novaes, Júlia
Let $\alpha$ be a given real number. It is shown that for a given $\alpha$-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by $\alpha$-affine minorants with a fixed number of
Externí odkaz:
http://arxiv.org/abs/2305.10501
Autor:
Hoehner, Steven
A Minkowski symmetral of an $\alpha$-concave function is introduced, and some of its fundamental properties are derived. It is shown that for a given $\alpha$-concave function, there exists a sequence of Minkowski symmetrizations that hypo-converges
Externí odkaz:
http://arxiv.org/abs/2301.12619
Publikováno v:
Involve 17 (2024) 311-325
This article is concerned with the problem of placing seven or eight points on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^3$ so that the surface area of the convex hull of the points is maximized. In each case, the solution is given for convex hul
Externí odkaz:
http://arxiv.org/abs/2212.12778
Autor:
Besau, Florian, Hoehner, Steven
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a restr
Externí odkaz:
http://arxiv.org/abs/2208.13927
Autor:
Hoehner, Steven, Ledford, Jeff
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived, including extrem
Externí odkaz:
http://arxiv.org/abs/2205.09096
An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive continuous density
Externí odkaz:
http://arxiv.org/abs/2202.01353
Autor:
Hoehner, Steven
Publikováno v:
Journal of Mathematical Analysis and Applications, Volume 505, Issue 2, 2022
For a convex body $K$ in $\mathbb{R}^n$, we introduce and study the extremal general affine surface areas, defined by \[ {\rm IS}_{\varphi}(K):=\sup_{K^\prime\subset K}{\rm as}_{\varphi}(K),\quad {\rm os}_{\psi}(K):=\inf_{K^\prime\supset K}{\rm as}_{
Externí odkaz:
http://arxiv.org/abs/2103.00294
This article focuses on the problem of analytically determining the optimal placement of five points on the unit sphere $\mathbb{S}^2$ so that the surface area of the convex hull of the points is maximized. It is shown that the optimal polyhedron has
Externí odkaz:
http://arxiv.org/abs/2005.13660