# Thalia Jeffres : K\{a}hler-Einstein Metrics with Edge Singularities

In this talk, I will describe some recent work carried out with Rafe Mazzeo and Yanir Rubinstein, regarding the existence and nature of solutions to the problem of K\"{a}hler-Einstein metrics of constant negative curvature with certain prescribed singularities along a divisor in a compact, complex manifold. Earlier work of Aubin and of Yau established for the smooth compact case that for negative curvature, there are no obstructions beyond the immediate observation that the first Chern class of $M$ must be positive. I will include a brief outline of the method of solution in the smooth case. Since the publication of these earlier works, study of the negative case has focused on extension to various noncompact settings. In the situation described here, we considered metrics with conical singularities along a divisor. The most prominent feature of these metrics is that they are incomplete. Solution of this problem became possible recently when Simon Donaldson achieved a breakthrough in the linear theory.

**Category**: Geometry and Topology**Duration**: 01:34:54**Date**: October 25, 2011 at 4:25 PM**Views**: 140-
**Tags:**seminar, Geometry/topology Seminar

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