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On curvature conditions using Wasserstein spaces
2014-08-05
[Electronic ed.]
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Universitätsbibliothek Leipzig
Universitätsbibliothek Leipzig, Leipzig
Fakultät für Mathematik und Informatik
male
Neubrandenburg
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 of the identification of the q-heat equation with the gradient flow of the Renyi (3-p)-Renyi entropy functional in the p-Wasserstein space is given. For that, a further study of the q-heat flow is presented including a condition for its mass preservation.
500
Wassersteinräume, verallgemeinter Ricci-Krümmung, q-Wärmefluss, Renyi-Entropie
Wasserstein spaces, generalized Ricci curvature, q-heat flow, Renyi entropy
urn:nbn:de:bsz:15-qucosa-149614
Universität Leipzig
dgg
Universität Leipzig, Leipzig
Martin
Kell
1985-09-19
aut
Jürgen
Jost
Professor
dgs
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Luigi
Ambrosio
Professor
rev
eng
2014-02-17
2014-07-22
born digital
With an application to the q-Laplace heat equation
Martin Kell
mail.mkell@gmail.com
doctoral_thesis