Zobrazeno 1 - 10
of 458
pro vyhledávání: '"52A21"'
Autor:
Lakos, Gyula
Assume that $\mathfrak A$ is a real Banach space of finite dimension $n\geq2$. Consider any Borel probability measure $\nu$ supported on the unit ball $K$ of $\mathfrak A$. We show that \[\Delta(\nu)=\int_{x \in K}\int_{ y\in K}|x-y|_{\mathfrak A} \,
Externí odkaz:
http://arxiv.org/abs/2411.14129
Autor:
Christensen, Erik
The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For posi
Externí odkaz:
http://arxiv.org/abs/2410.20112
We formulate a complex analog of the celebrated Levi-Hadwiger-Boltyanski illumination (or covering) conjecture for complex convex bodies in C^n, as well as its (non-comparable) fractional version. A key element in posing these problems is computing t
Externí odkaz:
http://arxiv.org/abs/2410.12021
For every $n \geq 2$, let $K_k^n$ denote the hyperspace of all $k$-dimensional closed convex subsets of the Euclidean space $R^n$ endowed with the Atouch-Wets topology. Let $ K_{k,b}^n$ be the subset of $K_k^n$ consisting of all $k$-dimensional compa
Externí odkaz:
http://arxiv.org/abs/2410.00839
We study inequalities on the volume of Minkowski sum in the class of anti-blocking bodies. We prove analogues of Pl\"unnecke-Ruzsa type inequality and V. Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We a
Externí odkaz:
http://arxiv.org/abs/2409.14214
Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santal\'o inequality in its functional form. Inspired by their method, based on the Fokker-Planck sem
Externí odkaz:
http://arxiv.org/abs/2409.05541
Autor:
Chirvasitu, Alexandru
We prove that (a) the sections space of a continuous unital subhomogeneous $C^*$ bundle over compact metrizable $X$ admits a finite-index expectation onto $C(X)$, answering a question of Blanchard-Gogi\'{c} (in the metrizable case); (b) such expectat
Externí odkaz:
http://arxiv.org/abs/2409.03531
The Minkowski problem in convex geometry concerns showing a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an active area of r
Externí odkaz:
http://arxiv.org/abs/2407.20064
Publikováno v:
Aequationes Math. 97 (2023), no.1, 147-160
We study the James constant $J(\mathbb{X})$, an important geometric quantity associated with a normed space $ \mathbb{X} $, and explore its connection with isosceles orthogonality $ \perp_I. $ The James constant is defined as $J(\mathbb{X}) := \sup\{
Externí odkaz:
http://arxiv.org/abs/2407.14475
Autor:
Sakaki, Makoto, Tanaka, Ryota
We discuss translation minimal surfaces, homothetical minimal surfaces, and separable minimal surfaces in the $3$-space with $2m$-norm.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2407.08896