走向现代数学学术报告 – 袁日荣副教授（No.994)

报告题目：On Fully Nonlinear Equations: A Priori Estimates and Structural Results

报 告 人：袁日荣 副教授（华南理工大学）

邀 请 人：王大斌 教授

报告时间：2026年11月9日 14：30

报告地点：东海岸校区D209

报告摘要：In this talk, I will present my work on fully nonlinear elliptic equations, divided into two main parts. In the first part, I will discuss my research on complex manifolds. By further developing the blow-up analysis originating from Dinew-Kołodziej and establishing a new property for 𝒞-subsolutions, I derive the -estimate for fully nonlinear elliptic equations on closed Hermitian manifolds under optimal structural conditions. Furthermore, I will talk about my results on the Dirichlet problem. In the second part, I will focus on the structural results for fully nonlinear equations. I will explain how these results provide new structural insights into these equations. Furthermore, I will demonstrate their applications to conformal geometry.

报告人简介： 袁日荣，博士毕业于厦门大学，现为华南理工大学数学学院副教授，主要从事完全非线性方程的研究。目前已在 Ann. PDE.、Adv. Math.、CVPDE、Comm. Anal. Geom. 等期刊上发表十余篇文章。