Geometric Flows of Diffeomorphisms
The idea of this thesis is to apply the methodology of geometric heat flows to the study of spaces of diffeomorphisms. We start by describing the general form that a geometrically natural flow must take and the implications this has for the evolution equations of associated geometric quantities. We discuss the difficulties involved in finding appropriate flows for the general case, and quickly restrict ourselves to the case of surfaces. In particular the main...[Show more]
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