Felix Lubbe and Andreas Hermann
|A Stability result for Mean Curvature Flow in Lorentzian Manifolds|
Given a Riemannian manifold M with bounded geometry, we consider its (graphical)
mean curvature flow inside the Lorentzian product manifold RxM.
If the initial graph is uniformly space-like and the solution has bounded
geometry, these conditions are preserved under the mean curvature flow.
Furthermore, if M=RxN, we obtain a convergence result for the flow
using barriers. This is joint work with Klaus Kröncke, Oliver Lindblad-Petersen,
Áron Szabó, Wolfgang Maurer, Oliver Schnürer, Tobias Marxen and Wolfgang Meiser.
|The mass of a compact Riemannian manifold|
Let (M,g) be a compact Riemannian manifold without boundary. Assume that the conformal Laplace operator L acting on smooth functions on M is strictly positive and that the metric g is flat on an open neighborhood of a point p in M. Then the mass m(g,p) of (M,g) at the point p is defined as the constant term in the expansion of the Green function of L at p. We prove a variational characterization of m(g,p) and give some applications to the ADM mass of an asymptically flat Riemannian manifold. This is joint work with Emmanuel Humbert.