Summer School »Between Geometry and Relativity« Mitschnitt einer Veranstaltung des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) am Mittwoch, dem 19. Juli 2017 im Lise Meitner-Hörsaal der Fakultät für Physik Teil 13: Richard Schoen: Positive Energy Theorems 5 Kamera: Lilian Nowak, Johannes Sauer, Daniel Winkler Schnitt: Daniel Winkler Abstract: We will introduce positive energy/mass problems in general relativity and discuss methods for solving some of them. The methods will involve minimal hypersurfaces and marginally outer trapped surfaces and require an understanding of existence problems as well as the second variation and stability notions for these hypersurfaces. We will also introduce Penrose inequalities which give stronger versions of positive energy theorems for black hole spacetimes. We will describe the flow approaches which have been developed to prove the Riemannian Penrose inequality. Richard Schoen ist Professor am Department of Mathematics der University of California. INHALT ====== Kapitel Titel Position --------------------------------------------------------------------- 1. Vorspann 00:00:00 2. Metrics on closed compact manifolds 00:00:10 3. Alternative approach to the metric problem 00:12:53 4. Eigenfunctions on hypersurfaces 00:24:02 5. Minimal k-slicings 00:33:40 6. Second fundamental forms. Scalar curvature 00:48:43

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