Work

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

Year: 2026

Type: preprint

Abstract: We resolve the long-standing problem of establishing interior \(C^2\) estimates for admissible solutions of the graphical scalar curvature equation in every dimension \(n\ge 3\). More precisely, we prove interior curvature estimates for admissible solutions to the constant graphical scalar curvature equation. The proof combines Jacobi inequalities with a two-surface maximum principle and a two-surface Pogorelov estimate.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02581

Authors: Qiu, Guohuan, Yan, Jin

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7207571619

Cites: 5

Cited by: 6

Related to: 10