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.
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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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