32 citations · 154 across the 12 of their papers we have counts for
18 papers
On the structure of RCD spaces with upper curvature bounds
Vitali Kapovitch, Martin Kell, Christian Ketterer
We develop a structure theory for RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is a topological manifold with boundary wh…
On the existence of dual solutions for Lorentzian cost functions
Martin Kell, Stefan Suhr
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under…
On quotients of spaces with Ricci curvature bounded below
Fernando Galaz-García, Martin Kell, Andrea Mondino +1
Let be a smooth Riemannian manifold and a compact Lie group acting on effectively and by isometries. It is well known that a lower bound of the sectional c…
Transport maps, non-branching sets of geodesics and measure rigidity
Martin Kell
In this paper we investigate the relationship between a general existence of transport maps of optimal couplings with absolutely continuous first marginal and the property of the b…
On the volume measure of non-smooth spaces with Ricci curvature bounded below
Martin Kell, Andrea Mondino
We prove that, given an -space , then it is possible to -essentially cover by measurable subsets with the following proper…
Symmetric orthogonality and non-expansive projections in metric spaces
Martin Kell
In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear to the metric setting…