Zobrazeno 1 - 10
of 317
pro vyhledávání: '"Lytchak, A"'
Autor:
Lytchak, Alexander, Wilking, Burkhard
We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of the base is
Externí odkaz:
http://arxiv.org/abs/2411.15324
Autor:
Lytchak, Alexander, Wagner, Sophia
We show that a length-minimizing disk inherites the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2308.14684
Autor:
Lytchak, Alexander
We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.
Comment: The depende
Comment: The depende
Externí odkaz:
http://arxiv.org/abs/2307.14284
Autor:
Lytchak, Alexander
We provide new structural results on sets of positive reach in Euclidean spaces and Riemannian manifolds.
Externí odkaz:
http://arxiv.org/abs/2302.05157
Autor:
Lytchak, Alexander
We discuss solutions of several questions concerning the geometry of conformal planes.
Comment: Bibliography corrected
Comment: Bibliography corrected
Externí odkaz:
http://arxiv.org/abs/2211.01347
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, Petrunin, Anton
Publikováno v:
Israel J. Math. 255 (2023), no. 2, 763--781
We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.
Externí odkaz:
http://arxiv.org/abs/2107.09295
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
Autor:
Lytchak, Alexander, Petrunin, Anton
Publikováno v:
J. Optim. Theory Appl. 194 (2022), no 2, 636--642
We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Ba\v{c}\'ak. Namely, we construct an example of convex subsets
Externí odkaz:
http://arxiv.org/abs/2104.09026
Autor:
Lytchak, Alexander, Petrunin, Anton
Publikováno v:
J. Reine Angew. Math. 782 (2022), 235--245
We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface. As a corollary we obtain peculiar properties that hold true for every convex set in any generic Riemannian manifold (M,g). For example, if
Externí odkaz:
http://arxiv.org/abs/2103.15189