Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
Guohuan Qiu, Jin Yan
Abstract
We resolve the long-standing problem of establishing interior \(C2\) estimates for admissible solutions of the graphical scalar curvature equation in every dimension \(n 3\). 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.
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