PreprintarXiv licencearXiv
Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
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.
Related
- Interior curvature estimates for graphical curvature quotient equations
- Interior curvature estimates for convex solutions of a prescribed curvature quotient equation
- Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides
- Interior gradient estimates for mean curvature equations on Riemannian manifolds
- A Comparison Pogorelov Estimate for Graphical σk-Curvature Equations
BibTeX
@misc{qiu2026interior,
title = {{Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions}},
author = {Guohuan Qiu and Jin Yan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02581},
eprint = {2609.02581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02581},
}
RIS
TY - UNPB
TI - Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
AU - Guohuan Qiu
AU - Jin Yan
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.02581
UR - https://arxiv.org/abs/2609.02581
AB - 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≥ 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.
ER -