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报告题 目：Hyperconvexity and Bergman functions: quantitative results

报告人：陈伯勇 教授（复旦大学）

摘要：A central problem in several complex variables is the Levi problem, which was solved mainly by Oka long time ago. According to a folklore viewpoint attributed to Oka, the next central problem in several complex variables is to understand the boundary behavior of the Bergman kernel on bounded pseudoconvex domains. The case of strongly pseudoconvex domains is well-understood through the deep work of Hormander and Fefferman. Much less is known for weakly pseudoconvex domains, or more generally, pseudoconvex domains with very wild boundaries. Hyperconvex domains appear as nice and very general models of pseudoconvex domains on which the Bergman kernel can be analyzed precisely.

In this talk, we shall survey some results around a longstanding conjecture that every bounded pseudoconvex domain with C⁰ boundary is hyperconvex, as well as quantitative estimates of Bergman functions on hyperconvex domains. Highlights are the author’s recent work that every bounded pseudoconvex domain with Hölder boundary is hyperconvex and every bounded pseudoconvex domain with C⁰ boundary admits an optimal lower bound for the Bergman kernel.

报告时间：2023年7月7日（周五）上午10:00-11:30

报告地点：首都师范大学本部校区教二楼 612 

报告人简介：复旦大学77779193永利官网陈伯勇教授，百篇优秀博士学位论文奖获得者，入选教育部新世纪优秀人才支持计划等。

邀请人: 张利友