Search Results - "Kell, Martin"

Transport maps, non-branching sets of geodesics and measure rigidity by Kell, Martin

“…In this paper we investigate the relationship between a general existence of transport maps of optimal couplings with absolutely continuous first marginal and…”
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Symmetric orthogonality and non-expansive projections in metric spaces by Kell, Martin

“…In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear…”
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Uniformly Convex Metric Spaces by Kell, Martin

“…In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit ageneralized convexity of the metric from a fixed point. Using a…”
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Representation of Markov chains by random maps: existence and regularity conditions by Jost, Jürgen, Kell, Martin, Rodrigues, Christian S.

“…We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved…”
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q-Heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space by Kell, Martin

“…Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014) [5], we show that the L2-gradient flow of the q-Cheeger energy, called q-heat flow, solves…”
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Sectional Curvature-Type Conditions on Metric Spaces by Kell, Martin

“…In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff…”
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On the structure of $$\mathrm {RCD}$$ spaces with upper curvature bounds by Kapovitch, Vitali, Kell, Martin, Ketterer, Christian

“…We develop a structure theory for $$\mathrm {RCD}$$ RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is…”
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On the structure of RCD spaces with upper curvature bounds by Kapovitch, Vitali, Kell, Martin, Ketterer, Christian

“…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…”
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A notion of nonpositive curvature for general metric spaces by Bačák, Miroslav, Hua, Bobo, Jost, Jürgen, Kell, Martin, Schikorra, Armin

“…We introduce a new definition of nonpositive curvature in metric spaces and study its relation to the existing notions of nonpositive curvature in comparison…”
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Transport maps, non-branching sets of geodesics and measure rigidity by Kell, Martin

“…In this paper we investigate the relationship between a general existence of transport maps of optimal couplings with absolutely continuous first marginal and…”
Get full text

Symmetric orthogonality and non-expansive projections in metric spaces by Kell, Martin

“…In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear…”
Get full text

Sectional curvature-type conditions on metric spaces by Kell, Martin

“…In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff…”
Get full text

On Cheeger and Sobolev differentials in metric measure spaces by Kell, Martin

“…Recently Gigli developed a Sobolev calculus on non-smooth spaces using module theory. In this paper it is shown that his theory fits nicely into the theory of…”
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On the existence of dual solutions for Lorentzian cost functions by Kell, Martin, Suhr, Stefan

“…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…”
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A note on non-negatively curved Berwald spaces by Kell, Martin

“…In this note it is shown that Berwald spaces admitting the same norm-preserving torsion-free affine connection have the same (weighted) Ricci curvatures…”
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Uniformly convex metric spaces by Kell, Martin

“…In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a…”
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On Interpolation and Curvature via Wasserstein Geodesics by Kell, Martin

“…In this article, a proof of the interpolation inequality along geodesics in $p$-Wasserstein spaces is given. This interpolation inequality was the main…”
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q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space by Kell, Martin

“…Based on the idea of a recent paper by Ambrosio-Gigli-Savar\'e in Invent. Math. (2013), we show that flow of the $q$-Cheeger energy, called $q$-heat flow,…”
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On the volume measure of non-smooth spaces with Ricci curvature bounded below by Kell, Martin, Mondino, Andrea

“…Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), no. 2, 593-610 We prove that, given an $RCD^{*}(K,N)$-space $(X,d,m)$, then it is possible to…”
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A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure Spaces by Kell, Martin

“…In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like…”
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