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pro vyhledávání: '"Alfonseca, M. Angeles"'
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
Following Santal\'{o}'s approach, we prove several characterizations of a disc among bodies of constant width, constant projections lengths, or constant section lengths on given families of geodesics.
Comment: 16 pages, 10 figures
Comment: 16 pages, 10 figures
Externí odkaz:
http://arxiv.org/abs/1910.10248
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
Akademický článek
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We construct examples of two convex bodies $K,L$ in $\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be rotated to be co
Externí odkaz:
http://arxiv.org/abs/1505.05817
Let $K$ and $L$ be two convex bodies in ${\mathbb R^4}$, such that their projections onto all $3$-dimensional subspaces are directly congruent. We prove that if the set of diameters of the bodies satisfy an additional condition and some projections d
Externí odkaz:
http://arxiv.org/abs/1412.2727
Autor:
Alfonseca, M. Angeles, Kim, Jaegil
Publikováno v:
Can. J. Math.-J. Can. Math. 67 (2015) 3-27
One of the fundamental results in Convex Geometry is Busemann's theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is only natural to ask if there is a quantitative version of Busemann's theorem, i.e., if
Externí odkaz:
http://arxiv.org/abs/1304.3359
Publikováno v:
Indiana University Mathematics Journal, 2017 Jan 01. 66(1), 275-296.
Externí odkaz:
https://www.jstor.org/stable/26318573
Autor:
Alfonseca, M. Angeles
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 August 2013 404(2):326-337
Publikováno v:
In Advances in Mathematics 20 March 2011 226(5):4533-4606