报告题目：Concavity Inequalities for k-Hessian Operators and Their Applications

报告人：董伟松教授 天津大学

报告时间：2026年10月31日 星期六 上午10:00 –11:00

报告地点：伍卓群楼第二报告厅

校内联系人:任长宇 [email protected]

报告摘要：

  This talk presents quantitative concavity inequalities for k-Hessian operators and their role in the regularity theory of fully nonlinear elliptic equations. After a brief review of related developments, we introduce the main inequalities under dynamic semi-convexity and explain the key ideas in their proofs. The approach combines recursive concavity identities, suitable decompositions of direction vectors, and higher-dimensional lifting to control third-order terms arising in second-order estimates. We also discuss corresponding concavity inequalities in the complex setting. Finally, we discuss applications to sum-of-Hessians equations and Hessian quotient equations.

报告人简介：

  董伟松，天津大学金沙娱乐城 教授，博士毕业于哈尔滨工业大学。主要研究兴趣为完全非线性椭圆方程。已在《Journal of Functional Analysis》、《Discrete and Continuous Dynamical Systems. Series A》、《Journal of Differential Equations》、《Revista Matematica Iberoamericana》、《Calc. Var. Partial Differential Equations》等期刊上发表论文多篇。主持国家自然科学基金青年基金项目一项。