Geometric Analysis Seminar —— Gauduchon Metrics and Hermite-Einstein Metrics on Non-Kähler Varieties
报告人：潘仲銘（Université du Québec à Montréal）
时间：2025-12-24 09:00-10:00
地点：online
【摘要】
Gauduchon metrics are very useful generalizations of Kähler metrics in non-Kähler geometry, as Gauduchon proved that these special metrics always exist on compact complex manifolds. One of their important applications is defining the notion of stability for vector bundles/sheaves on non-Kähler manifolds. It also leads to studying the existence of Hermite-Einstein metrics and the classification of non-Kähler surfaces. In this talk, I will first introduce a singular version of Gauduchon's theorem and its application to the Hermite-Einstein problem for stable reflexive sheaves on non-Kähler normal varieties. Then, I will explain one of the main technical points that lies in obtaining uniform Sobolev inequalities for perturbed hermitian metrics on a resolution of singularities.
【报告人简介】
Chung-Ming Pan is currently a postdoc at Université du Québec à Montréal. He obtained his Ph.D. at Université de Toulouse in 2023 under the supervision of Vincent Guedj and Henri Guenancia. His research focuses on complex geometry and differential geometry.
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