Research

My research is focused on on problems in geometric analysis arising (not only) in general relativity. In particular, I am interested in concepts of quasi-local mass in general relativity and other quasi-local quantities. Further research interests are surfaces satisfying certain curvature conditions such as prescribed mean curvature or higher order equations for the curvature. These problems are related to various geometric PDEs of elliptic or parabolic type.

Most recently I study surfaces that are critical points for the Willmore functional subject to an area constraint. The goal of this ongoing project is to understand the aspects of the interaction of these surfaces with the ambient geometry.

Another main topic is the analysis of marginally outer trapped surfaces in initial data sets for the Einstein equations. Such surfaces can be understood as the quasi-local trace of a black hole in the developing space-time.

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