24.04.2014, 16:15 Uhr  –  University of Potsdam, Neues Palais, Haus 9, Room 1.14
Seminar "Topics in Geometric Analysis"

Tobias Lamm and Christopher Nerz

16:15 Uhr Tobias Lamm (KIT Karlsruhe) Optimal rigidity estimates for nearly umbilical surfaces in arbitrary codimension

In this talk we describe recent joint work with R. Schätzle in which we extend a rigidity result of DeLellis and Müller to arbitrary codimensions. More precisely, we show that every immersion of a two-dimensional surface into $\mathbb{R}^n$, whose tracefree second fundamental form is small in $L^2$ has to be close to a round sphere in the $W^{2,2}$-norm.

 
17:45 Uhr Christopher Nerz (Universität Tübingen) Foliations of asymptotically flat manifolds and their time evolution

For the study of asymptotically flat manifolds in mathematical general relativity, surfaces of constant mean curvature (CMC) haven proved to be a useful tool. In 1996, Huisken-Yau showed that any asymptotically flat Riemannian manifold can be uniquely foliated by closed CMC surfaces. Furthermore, they interpreted this foliation as a definition of the center of mass. We prove that this definition is compatible with the definition of linear momentum by Arnowitt-Deser-Misner: The evolution of this foliation (asymptotically) corresponds to a translation with direction given by the quotient of (ADM) linear momentum and mass - equivalent to the center of mass in Newtonian systems.

 
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