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1	On curvature conditions using Wasserstein spaces Kell, Martin 05 August 2014 (has links) (PDF) 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. Wassersteinräume verallgemeinter Ricci-Krümmung q-Wärmefluss Renyi-Entropie Wasserstein spaces generalized Ricci curvature q-heat flow Renyi entropy ddc:500
2	On curvature conditions using Wasserstein spaces Kell, Martin 22 July 2014 (has links) 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. info:eu-repo/classification/ddc/500 ddc:500