Скачать или смотреть Rafe Mazzeo - Minicourse - Lecture 5

Rafe Mazzeo
Conic metrics on surfaces with constant curvature

An old theme in geometry involves the study of constant curvature metrics on surfaces with isolated conic singularities and with prescribed cone angles. This has been studied from many points of view, ranging from synthetic geometry to geometric analysis to algebraic geometry to calculus of variations. I will describe some of this, with notable recent highlights by Mondello-Panov and Kapovich and Dey, but ultimately focus on some recent work with Xuwen Zhu, based on my earlier work with Weiss, concerning the complicated stratified structure of the moduli space ofthese metrics, and the analytic problem of obtaining an unobstructed deformation problem.