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Minimal Surfaces and the Positive Mass Theorem

Student-Run Geometry/Topology Seminar

Speaker: Brian Harvie, UC Davis
Location: 2112 MSB
Start time: Thu, Nov 30 2017, 2:10PM

Minimal surface theory arises from the study of Plateau's problem, which physically manifests itself in the formation of soap films on a closed loop of wire. Following the resolution of the classical Plateau problem in 1930, generalizations to Riemannian Manifolds have produced a number of important applications. Possibly the most notable of these comes in Schoen and Yau's 1979 proof of the Positive Mass Theorem of General Relativity. In this talk we will: (1) review definitions and formulations for minimal surfaces, (2) state the Positive Mass Theorem for n=3, and (3) bridge these topics by explaining the use of (1) in the proof of (2). Some familiarity with basic notions from differential geometry (e.g. Tensor fields) is helpful but not required.