Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Stadler, Stephan"'
Autor:
Stadler, Stephan
We characterize higher rank model geometries -- Riemannian symmetric spaces, Euclidean buildings and products -- among Hadamard spaces by using antipodal sets at infinity.
Comment: arXiv admin note: text overlap with arXiv:2212.07092
Comment: arXiv admin note: text overlap with arXiv:2212.07092
Externí odkaz:
http://arxiv.org/abs/2405.16238
Autor:
Stadler, Stephan, Wenger, Stefan
The Dehn function of a metric space measures the area necessary in order to fill a closed curve of controlled length by a disc. As a main result, we prove that a length space has curvature bounded above by $\kappa$ in the sense of Alexandrov if and o
Externí odkaz:
http://arxiv.org/abs/2309.11329
Autor:
Stadler, Stephan
If a group $\Gamma$ acts geometrically on a CAT(0) space $X$ without 3-flats, then either $X$ contains a $\Gamma$-periodic geodesic which does not bound a flat half-plane, or else $X$ is a rank 2 Riemannian symmetric space, a 2-dimensional Euclidean
Externí odkaz:
http://arxiv.org/abs/2212.07100
Autor:
Stadler, Stephan
This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let $X$ be a CAT(0) space with a geometric group action. Suppose that every geodesic in $X$ lies in an $n$-flat, $n\geq 2$. If $X$ con
Externí odkaz:
http://arxiv.org/abs/2212.07092
Autor:
Petrunin, Anton, Stadler, Stephan
Publikováno v:
Amer. Math. Monthly, 131 (2024), no. 3, 239--251
We sketch several proofs of F\'ary--Milnor theorem.
Comment: 13 pages, 13 figures
Comment: 13 pages, 13 figures
Externí odkaz:
http://arxiv.org/abs/2203.15137
Autor:
Stadler, Stephan
Ballmann's Rank Rigidity Conjecture predicts that a CAT(0) space of higher rank with a geometric group action is rigid -- isometric to a Riemannian symmetric space, a Euclidean building, or splits as a direct product. We confirm this conjecture in ra
Externí odkaz:
http://arxiv.org/abs/2202.02302
We prove that a topological 4-manifold of globally non-positive curvature is homeomorphic to Euclidean space.
Externí odkaz:
http://arxiv.org/abs/2109.09438
Autor:
Lytchak, Alexander, Stadler, Stephan
We show that closed subsets with vanishing first homology in two-dimensional spaces inherit the upper curvature bound from their ambient spaces and discuss topological applications.
Externí odkaz:
http://arxiv.org/abs/2105.00726
This is the second in a two part series of papers concerning Morse quasiflats - higher dimensional analogs of Morse quasigeodesics. Our focus here is on their asymptotic structure. In metric spaces with convex geodesic bicombings, we prove asymptotic
Externí odkaz:
http://arxiv.org/abs/2003.08912
This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate assumptions on t
Externí odkaz:
http://arxiv.org/abs/1911.04656