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pro vyhledávání: '"Kell, Martin"'
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 whose interior is equal to the set of regular points. Further the set of
Externí odkaz:
http://arxiv.org/abs/1908.07036
Autor:
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 optimal coupling. Under natural assumptions dual solutions are established. It is further sho
Externí odkaz:
http://arxiv.org/abs/1808.04393
Autor:
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 the property of the background measure called essentially non-branching introduced by Rajal
Externí odkaz:
http://arxiv.org/abs/1704.05422
Publikováno v:
Journal of Functional Analysis, Volume 275, Issue 6, 15 September 2018, Pages 1368-1446
Let $(M,g)$ be a smooth Riemannian manifold and $\mathsf{G}$ a compact Lie group acting on $M$ effectively and by isometries. It is well known that a lower bound of the sectional curvature of $(M,g)$ is again a bound for the curvature of the quotient
Externí odkaz:
http://arxiv.org/abs/1704.05428
Autor:
Kell, Martin
This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces is defined. In the second part of the thesis a proof o
Externí odkaz:
https://ul.qucosa.de/id/qucosa%3A12801
https://ul.qucosa.de/api/qucosa%3A12801/attachment/ATT-0/
https://ul.qucosa.de/api/qucosa%3A12801/attachment/ATT-0/
Autor:
Kell, Martin, Mondino, Andrea
Publikováno v:
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 $m$-essentially cover $X$ by measurable subsets $(R_{i})_{i\in \mathbb{N}}$ with the following property: for each $i$ there exists $k_{i} \in \mathbb{N}\cap [1,N]$ such th
Externí odkaz:
http://arxiv.org/abs/1607.02036
Autor:
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 to the metric setting. If the space has non-positive curvature in the sense Busemann then i
Externí odkaz:
http://arxiv.org/abs/1604.01993
Autor:
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 measure of a Busemann concave space is non-trivial then the space is doubling and satisfies a Po
Externí odkaz:
http://arxiv.org/abs/1601.03363
Autor:
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 differentiability spaces initiated by Cheeger, Keith and others. A relaxation procedure for
Externí odkaz:
http://arxiv.org/abs/1512.00828
Autor:
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. Combing this with Szab\'o's Berwald metrization theorem one can apply the Cheeger-Gromoll splitt
Externí odkaz:
http://arxiv.org/abs/1502.03764