28 mar 2023 -- 14:30
Sala Orsi, Dipartimento di Matematica "G. Peano", Torino
Differential Geometry Seminar Torino
Abstract.
In this lecture, we show how the classical divergence theorem joint with geometric identities can be used to obtain rigidity results on Riemannian manifolds. First, we introduce a generalized Pohozaev Identity that can be applied to problems involving metrics which satisfy overdetermined conditions, such as static and Einstein-type metrics. These have interesting applications to General Relativity and Geometric flows. In particular, in the compact case we obtain rigidity results for the hemisphere and geodesic balls in space forms. Lastly, we show how a version of the divergence theorem can be used to study the existence of free-boundary hypersurfaces in domains whose boundary is a regular level set.
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If you would like to attend the talk remotely, please send an e-mail to dgseminar.torino@gmail.com