Zobrazeno 1 - 10
of 328
pro vyhledávání: '"I Florentin"'
In this note we study caustic-free regions for convex billiard tables in the hyperbolic plane or the hemisphere. In particular, following a result by Gutkin and Katok in the Euclidean case, we estimate the size of such regions in terms of the geometr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f467ff43da5a972e123bafcaf6854812
Publikováno v:
Nonlinearity
In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth centrally symmetric and strictly convex body $K$, for every convex caustic which $K$ possesses, the "dual" billiard dyn
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77c222cff1cbf6f8a5af9c91662df902
https://doi.org/10.1088/1361-6544/aa9d5c
https://doi.org/10.1088/1361-6544/aa9d5c
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb2075f0631d05f0e1ba0232f1079d4c
Autor:
Alexander Segal, Dan I. Florentin
Publikováno v:
Geometriae Dedicata. 184:115-119
We provide sharp upper bounds for the number of symmetrizations required to transform a star shaped set in \({\mathbb {R}}^n\) arbitrarily close (in the Hausdorff metric) to the Euclidean ball.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::143cda5a06cdaa3dcfcd0ba8e9907840
https://doi.org/10.1007/s10711-016-0159-z
https://doi.org/10.1007/s10711-016-0159-z
Publikováno v:
Proceedings of the American Mathematical Society. 144:2197-2204
The striking analogy between mixed volumes of convex bodies and mixed discriminants of positive semidefinite matrices has repeatedly been observed. It was A. D. Aleksandrov [1] who, in his second proof of the Aleksandrov–Fenchel inequalities for th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7ad478baac3b8c47a290a60b8ed56249
https://doi.org/10.1090/proc/12344
https://doi.org/10.1090/proc/12344
Publikováno v:
Geometriae Dedicata. 178:337-350
We provide a natural generalization of a geometric conjecture of Fary and Redei regarding the volume of the convex hull of \(K \subset {\mathbb {R}}^n\), and its negative image \(-K\). We show that it implies Godbersen’s conjecture regarding the mi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::913c2d8709a9b7626dbb639742a50579
https://doi.org/10.1007/s10711-015-0060-1
https://doi.org/10.1007/s10711-015-0060-1
Autor:
Dan I. Florentin, Alexander Segal
Publikováno v:
International Mathematics Research Notices.
We present a direct analytic method towards an estimate for the rate of convergence (to the Euclidean Ball) of Steiner symmetrizations. To this end we present a modified version of a known stability property of the Steiner symmetrization.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::94febac3feb99bd6296909c3b56db42c
https://doi.org/10.1093/imrn/rnx154
https://doi.org/10.1093/imrn/rnx154
Publikováno v:
Advances in Mathematics
We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical inf-convolution, this type of inequality is called the Prekopa-Leindler
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba6fe80f20f2ec1237b5880e774e366f
Publikováno v:
Electronic Research Announcements in Mathematical Sciences. 18:112-118
We characterize order preserving transforms on the class of lower-semi-continuous convex functions that are defined on a convex subset of $\mathbb{R}^n$ (a "window") and some of its variants. To this end, we investigate convexity preserving maps on s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::71dc0e65c6286a4b4dd64045b6dd7dbc
https://doi.org/10.3934/era.2011.18.112
https://doi.org/10.3934/era.2011.18.112