Construction of Riemannian geometries with prescribed scalar curvature and with monotonous Geroch mass

Events

Presentation Name：	Construction of Riemannian geometries with prescribed scalar curvature and with monotonous Geroch mass
Presenter：	Dr.István Rácz
Date：	2019-10-21
Location：	光华东主楼1501
Abstract：	Consider a smooth three-dimensional manifold $/Sigma$ that is smoothly foliated by topological two-spheres. Choose a smooth flow such that the integral curves of it intersect the foliating two-spheres precisely once. Assume that a smooth distribution of induced two-metrics on the leaves of the foliation is also chosen such that the area of the leaves is non-decreasing. It is shown then that a large variety of Riemannian three-metrics, with freely specifiable scalar curvature, can be constructed on $/Sigma$ such that the foliation we started with gets to be an inverse mean curvature foliation, the prescribed flow turns out to be a generalized inverse mean curvature flow and the Geroch mass---defined with respect to the foliation---is guaranteed to be non-decreasing. 海报
Annual Speech Directory：	No.220

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