报告题目：Global Curvature Estimates for
Curvature Equations with 
报告人：闫谨博士 中国科学院数学与系统科学研究院
报告时间：2026年10月23日 星期五 上午10:00 –11:00
报告地点：数学楼第二报告厅
校内联系人:任长宇[email protected]
报告摘要：
For  , we obtain global curvature estimates for closed star-shaped
 -convex hypersurfaces satisfyingwith a general positive right-hand side, together with the corresponding global-to-boundary estimates for Euclidean Hessian equations. These estimates answer a question posed by Guan–Li–Li in this range of
; the result is new for  .
|
The key ingredient is a new concavity inequality for the elementary symmetric function
, which controls the spectral quadratic form arising from the second variation of
. The proof is based on an easy–hard decomposition of the spectral variables. The easy region is treated using an optimal constrained concavity estimate for
, whereas the hard region is analyzed through Gårding-root coordinates and the concavity of the ordered partial sums of the inverse roots.
报告人简介：闫谨，中国科学院数学与系统科学研究院数学研究所博士后，主要从事完全非线性偏微分方程与几何分析研究。在Journal of Differential Equations、Advanced Nonlinear Studies和Journal of Partial Differential Equations等知名学术期刊发表论文。
