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On curvature conditions using Wasserstein spaces

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-149614
Date05 August 2014
CreatorsKell, Martin
ContributorsUniversität Leipzig, Fakultät für Mathematik und Informatik, Professor Jürgen Jost, Professor Luigi Ambrosio, Professor Jürgen Jost
PublisherUniversitätsbibliothek Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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