3 papers
math.DG2019
Improvements of upper curvature bounds
Alexander Lytchak, Stephan Stadler
We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.
math.DG2018
Ricci curvature in dimension 2
Alexander Lytchak, Stephan Stadler
We prove that in two dimensions the synthetic notions of lower bounds on sectional and on Ricci curvature coincide.
math.DG2017
Conformal deformations of CAT(0) spaces
Alexander Lytchak, Stephan Stadler
We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.