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A general approach to stability of the soap bubble theorem and related problems

PD Dr. Julian Scheuer

Mittwoch, 2020-10-21 08:30Uhr

The soap bubble theorem says that a closed, embedded surface of the Euclidean space with constant mean curvature must be a round sphere. Especially in real-life problems it is of importance whether and to what extent this phenomenon is stable, i.e. when a surface with almost constant mean curvature is close to a sphere. This problem has been receiving lots of attention until today. The purpose of this talk is to discuss two different approaches to problems of this type. The first one is a new general approach based on stability of the so-called "Nabelpunktsatz". The second one is of variational nature and employs the theory of curvature flows.