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Geometry and Topology Seminar - The entropy differential for minimal surfaces

Mike Deutsch, Department of Mathematics, Washington University in St. Louis

January 25, 2013 - 4:00 pm to 5:00 pm
Location: Cupples I, Room 8 | Host: Prof. Xiang Tang

Abstract:  The entropy functional is a natural geometric object that first occurred in Hamiliton's early work on Ricci flow.  In the case of surfaces, it was noticed very recently that the Euler-Lagrange equations for this functional lead to a quadratic differential, called the "entropy differential" in the paper by Bernstein and Mettler (arxiv.org/abs/1301.1663), which is holomorphic on minimal surfaces.  We will briefly discuss a number of results from that paper, plus a simple corollary of our own: minimal surface in R³ is determined by its Hopf and entropy differentials up to a certain isothermic transformation known as the Goursat transform.