湖南大学偏微分方程系列报告
会议时间：2022/12/12（周一） 10:00-12:00 (GMT+08:00) 中国标准时间 - 北京
会议腾讯ID：306-449-267
报告人：关波 教授 （The Ohio State University）
邀请人：徐露
报告题目：Prescribed volume forms in Apelli cohomology groups on compact Hermitian manifolds
报告摘要：Given a strongly positive (p, p) form Ω on a Hermitian manifold (Mn , ω) of dimension n ≥ 2, where 1 ≤ p < n is an integer, we study the problem of finding a strongly positive (p, p) form in the Apelli cohomology class of Ω with prescribed volume form. For p = 1, this is equivalent to the classical Calabi conjecture solved by S.T. Yau in the K¨ahler case, while for p = n − 1 it corresponds to the Gauduchon conjecture proved by Szekelyhidi-Tosatti-Weinkove more recently. From the PDE point of view, this leads to a new fully nonlinear elliptic equation which falls outside the framework developed by Cafferlli-Nirenberg-Spruck. We shall treat a general class of PDEs which also arise from other geometric problems. The talk is based on work with my student Mathew George.
报告人简介：关波，俄亥俄州立大学数学系教授。研究方向为非线性偏微分方程和几何分析, 主要工作包括一般区域/流形上实和复蒙日-安培方程；常高斯曲率曲面的普拉图问题；闵可夫斯基问题的推广；关于双曲空间中具有常曲率和给定渐近边界的完备曲面的研究；以及实或复流形上一般完全非线性偏微分方程。其代表作发表在 Adv. Math., Amer. J. Math., Annals of Math., CPAM, Duke Math. J., JDG, J. Eur. Math. Soc., J. Reine Angew. Math.等国际一流期刊上。
