Faculties of University Bonn: Search
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Gluing of metric measure spaces and the heat equation with homogeneous Dirichlet boundary values
(2020-07-09)
The first part of this thesis deals with gluing together several copies of an open subset of a metric measure space along the complement. This construction results in a metric measure space. We identify the Cheeger energy ......
Joint methods in imaging based on diffuse image representations
(2010-08-31)
This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or ...
Ricci curvature and gradient flows of the entropy for jump processes
(2013-04-03)
In the first part of this thesis, we present a new notion of Ricci curvature that applies to finite Markov chains. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott--Villani ...