中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：王斌（香港中文大学）
题 目：Global Curvature Estimates for Hessian Type Equations
时 间：2024.05.16（星期四）20:00-21:00
地 点：N813
摘 要：We derive global curvature estimates for closed strictly star-shaped (n-2)-convex hypersurfaces in warped product spaces, satisfying the prescribed (n-2)-curvature equation with a general right-hand side. The proof is inspired by the recent breakthrough of [Guan-Ren-Wang CPAM 2015] and it can be readily adapted to establish curvature estimates for semi-convex and (k+1)-convex solutions to the general k-curvature equation; it can also be used to prove the same estimates for prescribed curvature measure type equations. Furthermore, we briefly discuss the same problem for another class of Hessian type equations, which was initiated in [Chu-Jiao CVPDE 2021]. This talk is based on our recent work in progress, the current draft is available upon request.
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