Mathematics Colloquium

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Conformal Metrics of Prescribed Gauss Curvature

Speaker: Michael Struwe, ETH Zurich

Location: Warren Weaver Hall 1302

Date: Monday, October 8, 2012, 3:45 p.m.

Synopsis:

Given a Riemann surface \(\left ( M,g_0 \right )\), viewed as a two-dimensional Riemannian manifold with background metric \(g_0\), a classical problem in differential geometry is to determine what smooth functions \(f\) on \(M\) arise as the Gauss curvature of a conformal metric on \(M\). When \(M = S^2\) this is the famous Nirenberg problem. In fact, even when \(\left ( M,g_0 \right )\) is closed and has genus greater than 1, this question so far has not been completely settled. In my talk I will present some new results for this problem.