Hessian estimates for the sigma-2 equation in dimension four

• 成果类型: Article
• 署名作者: Shankar, Ravi; Yuan, Yu
• 署名单位: Princeton University; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2025.201.2.4
• 发表日期: 2025-03
• 页码: 489-513
• 关键词: k -Hessian equation; interior estimates and regularity; dirichlet problem; convex solutions; REGULARITY

摘要

We derive a priori interior Hessian estimates and interior regularity for the sigma 2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n >= 5) dimensions.