Zobrazeno 1 - 10
of 89
pro vyhledávání: '"52A20, 52A40"'
This article introduces the $L_p$-Gauss dual curvature measure and proposes its related $L_p$-Gauss dual Minkowski problem as: for $p,q\in\mathbb{R}$, under what necessary and/or sufficient condition on a non-zero finite Borel measure $\mu$ on unit s
Externí odkaz:
http://arxiv.org/abs/2412.13557
Autor:
Mussnig, Fabian, Ulivelli, Jacopo
We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saor\'in G
Externí odkaz:
http://arxiv.org/abs/2412.05001
Autor:
Saroglou, Christos, Wannerer, Thomas
In this paper, we extend two celebrated inequalities by Busemann -- the random simplex inequality and the intersection inequality -- to both complex and quaternionic vector spaces. Our proof leverages a monotonicity property under symmetrization with
Externí odkaz:
http://arxiv.org/abs/2409.01057
For every large enough $n$, we explicitly construct a body of constant width $2$ that has volume less than $0.9^n \text{Vol}(\mathbb{B}^{n}$), where $\mathbb{B}^{n}$ is the unit ball in $\mathbb{R}^{n}$. This answers a question of O.~Schramm.
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Externí odkaz:
http://arxiv.org/abs/2405.18501
We construct a convex body $K$ in $\mathbb{R}^n$, $n \geq 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K\cap H$ coincides with $c(K)$. This provides answers to
Externí odkaz:
http://arxiv.org/abs/2404.15188
Autor:
Ahn, Jonghyeon, Kerman, Ely
In this work we investigate subsets of $\mathbb{R}^{2n}$ with the property that their mean width can not be decreased by the action of natural classes of symplectomorphisms. A common theme of our results is that toric symmetry is a preferred feature
Externí odkaz:
http://arxiv.org/abs/2311.02870
Autor:
Prymak, Andriy, Singh, Jaskaran
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the geometry of the
Externí odkaz:
http://arxiv.org/abs/2311.00912
Autor:
Braides, Andrea, Chambolle, Antonin
Publikováno v:
Tunisian J. Math. 6 (2024) 299-319
We give an interpretation of a class of discrete-to-continuum results for Ising systems using the theory of zonoids. We define the classes of rational zonotopes and zonoids, as those of the Wulff shapes of perimeters obtained as limits of finite-rang
Externí odkaz:
http://arxiv.org/abs/2305.11054
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:
Berestovskii, V. N., Nikonorov, Yu. G.
The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We classified perfect and almost perfect polytopes among all regular polytopes and all semiregular polytopes excepting Archimedean solids and two four-dimen
Externí odkaz:
http://arxiv.org/abs/2304.12211