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pro vyhledávání: '"Yaskin, V."'
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
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2024 529(2)
Let $f$ be an integrable log-concave function on ${\mathbb R^n}$ with the center of mass at the origin. We show that $\int\limits_0^{\infty}f(s\theta)ds\ge e^{-n}\int\limits_{-\infty}^{\infty}f(s\theta)ds$ for every $ \theta\in S^{n-1}$, and the cons
Externí odkaz:
http://arxiv.org/abs/1706.02373
Autor:
Yaskin, V.
We disprove a conjecture of A. Koldobsky asking whether it is enough to compare $(n-2)$-derivatives of the projection functions of two symmetric convex bodies in the Shephard problem in order to get a positive answer in all dimensions.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/0707.1476
Autor:
Yaskin, V.
Let $\mathcal I_k$ be the class of convex $k$-intersection bodies in $\mathbb{R}^n$ (in the sense of Koldobsky) and $\mathcal I_k^m$ be the class of convex origin-symmetric bodies all of whose $m$-dimensional central sections are $k$-intersection bod
Externí odkaz:
http://arxiv.org/abs/0707.1471
Autor:
Yaskin, V.
The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in $\mathbb{R}^n$ with smaller volume of all $k$-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this questi
Externí odkaz:
http://arxiv.org/abs/math/0503289
Suppose that we have the unit Euclidean ball in $\R^n$ and construct new bodies using three operations - linear transformations, closure in the radial metric and multiplicative summation defined by $\|x\|_{K+_0L} = \sqrt{\|x\|_K\|x\|_L}.$ We prove th
Externí odkaz:
http://arxiv.org/abs/math/0412371
Autor:
Yaskin, V.
The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer to this problem is affirmative if $n\le 4$
Externí odkaz:
http://arxiv.org/abs/math/0410501
The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer is affirmative if $n\le 4$ and negative if
Externí odkaz:
http://arxiv.org/abs/math/0410496