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爱游戏体育平台冠名马竞:20221212 关波 Prescribed volume forms in Apelli cohomology groups on compact Hermitian manifolds

发布时间:2022-12-12 11:43    浏览次数:    来源:

爱游戏体育平台冠名马竞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 ? on a Hermitian manifold (Mn , ω) of dimension n ≥ 2, where 1 ≤ p < n is an integer, we study the problem of ?nding a strongly positive (p, p) form in the Apelli cohomology class of ? 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 Ca?erlli-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。


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