Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Ryabogin, Dmitry"'
We prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of its boundary to an arbitrary direction does not exceed $\frac{1}{6}$ of the body width in this direction. It follows that the di
Externí odkaz:
http://arxiv.org/abs/2305.15646
A bounded domain $K \subset \mathbb R^n$ is called polynomially integrable if the $(n-1)$-dimensional volume of the intersection $K$ with a hyperplane $\Pi$ polynomially depends on the distance from $\Pi$ to the origin. It was proved in [7] that ther
Externí odkaz:
http://arxiv.org/abs/2211.12693
Autor:
Ryabogin, Dmitry
We give a negative answer to Ulam's Problem 19 from the Scottish Book asking {\it is a solid of uniform density which will float in water in every position a sphere?} Assuming that the density of water is $1$, we show that there exists a strictly con
Externí odkaz:
http://arxiv.org/abs/2102.01787
We show that the fifth and the eighth Busemann-Petty problems have positive solutions for bodies that are sufficiently close to the Euclidean ball in the Banach-Mazur distance.
Comment: 25 pages, 2 figures
Comment: 25 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2101.08384
Autor:
Ryabogin, Dmitry
Let $d\ge 2$ and let $K$ and $L$ be two convex bodies in ${\mathbb R^d}$ such that $L\subset \textrm{int}\,K$ and the boundary of $L$ does not contain a segment. If $K$ and $L$ satisfy the $(d+1)$-equichordal property, i.e., for any line $l$ supporti
Externí odkaz:
http://arxiv.org/abs/2010.09864
Autor:
Ryabogin, Dmitry
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
Comment: 6 figures, 16 pages
Comment: 6 figures, 16 pages
Externí odkaz:
http://arxiv.org/abs/2010.09565
Let $K$ and $L$ be two convex bodies in ${\mathbb R^5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rota
Externí odkaz:
http://arxiv.org/abs/1801.08987
We prove that for every convex body $K$ with the center of mass at the origin and every $\varepsilon\in \left(0,\frac{1}{2}\right)$, there exists a convex polytope $P$ with at most $e^{O(d)}\varepsilon^{-\frac{d-1}{2}}$ vertices such that $(1-\vareps
Externí odkaz:
http://arxiv.org/abs/1705.01867
Akademický článek
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We say that a star body $K$ is completely symmetric if it has centroid at the origin and its symmetry group $G$ forces any ellipsoid whose symmetry group contains $G$, to be a ball. In this short note, we prove that if all central sections of a star
Externí odkaz:
http://arxiv.org/abs/1611.09443