Geometry/topology Seminar
Thursday, March 9, 2017, 12:00pm, 205 Physics
Carla Cederbaum (Tubingen University)
On extensions of CMC-Bartnik data
Abstract:- Bartnik data are a Riemannian 2-sphere of positive Gaussian curvature equipped with a non-negative function H to be thought of as its mean curvature in an ambient Riemannian 3-manifold. Mantoulidis and Schoen suggested a construction of asymptotically flat Riemannian 3-manifolds of non-negative scalar curvature which allow to isometrically embed given Bartnik data of vanishing mean curvature, i.e. H=0. They use their construction to explore and disprove stability of the Riemannian Penrose inequality. We adapt their construction to constant mean curvature (CMC) Bartnik data, i.e. H=const.>0. I will present the construction as well as the motivation for such a construction which is related to Bartniks quasi-local capacity/mass functional and its minimizing properties.
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