46 citations · 317 across the 42 of their papers we have counts for
58 papers
Lower curvature bounds on metric surfaces via the Bishop--Gromov inequality
Alexander Lytchak, Stephan Stadler
We characterize lower curvature bounds on metric surfaces by the Bishop--Gromov inequality for metric balls.
A question of Ulam and a theorem of de Rham
Alexander Lytchak
We generalize de Rham's decomposition theorem to proper metric spaces: every proper metric space has a unique decomposition as the product of a Euclidean space and a finite or coun…
Existence of least-area discs
Alexander Lytchak, Stephan Stadler
We prove that every closed Lipschitz curve in Euclidean space extends to a Lipschitz disc of least area, with Lipschitz constant controlled by that of the boundary curve. Our proof…
Non-compact convex hulls in CAT(0) spaces revisited
Alexander Lytchak
We simplify Goodwin's construction of a non-compact closed convex hull in a CAT(0) space and show that three points suffice for the example.
Dimension of CAT spaces
Alexander Lytchak
We prove that the covering dimension of a metric space with curvature bounded above equals its geometric dimension, without a separability assumption. This resolves a conjecture fo…
Hilbert space factor of metric spaces
Thomas Foertsch, Alexander Lytchak, Elefterios Soultanis
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off li…