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学术报告
学术报告
威尼斯官方网站登录百年校庆威尼斯官方网站系列学术报告之二十 俄亥俄州立大学关波教授报告通知
发布人:许美玲??威尼斯官方网站:2019-06-17?? 浏览次数:294

俄亥俄州立大学关波教授将于近日来访我校,做完全非线性椭圆方程方向的报告,以下是报告信息,欢迎感兴趣的师生参加。

  

时间:2019617(星期一) 15:30-16:30

地点:格物楼503

题目:Fully nonlinear elliptic equations for conformal deformation of Chern-Ricci curvatures

  

摘要:There are several ways to define Chern-Ricci curvatures for the Chern connection on a non-Kahler Hermitian manifold. We introduce a notion of mixed-Chern-Ricci forms, which naturally occur in geometric problems and seem interesting to study, and consider fully nonlinear elliptic equations for their conformal deformation. We establish a priori estimates and prove existence results for these equations under very general structure conditions.

Our work is motivated by the close connections of these equations to problems in non-Kahler complex geometry, and the fact that there have been increasing interests in fully nonlinear pde's beyond the complex Monge-Ampere equation from complex geometry. This talk is based on work with Chunhui Qiu and Rirong Yuan.

  

报告人简介关波,俄亥俄州立大学(Ohio State University)教授,博士毕业于University of Massachusetts,师从偏微分方程和几何分析专家Joel Spruck教授。通过假定某种下解存在,关波教授使用最少的结构条件,建立了最广泛意义下的完全非线性椭圆与抛物方程的解的存在性和正则性理论,极大地推进了Luis Caffarelli, Louis NirenbergJoel Spruck等人在欧式空间中具有几何约束边界的区域上的工作。关教授的工作涉及实或复的Monge-Ampere方程、Hessian型方程、曲率方程,并可以用来解决一系列重要的几何问题。


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