PreprintarXiv licencearXiv
Interior curvature estimates for convex solutions of a prescribed curvature quotient equation
Abstract
In this note, we prove a priori interior curvature bounds for convex solutions to an elliptic Weingarten curvature quotient equation. The proof avoids integral estimates, doubling inequalities and compactness arguments. It relies on a concavity inequality for the equation operator and a novel choice of the auxiliary function to carry out an elementary maximum-principle argument. As an application, we obtain interior curvature bounds for convex solutions of a prescribed special Lagrangian curvature equation in dimensions three and four.
Related
- Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides
- Interior curvature estimates for graphical curvature quotient equations
- Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
- Interior gradient estimates for mean curvature equations on Riemannian manifolds
- Curvature Estimates and Prescribed Curvature Problems for Sum Hessian Equations on Star-Shaped Hypersurfaces
BibTeX
@misc{wang2026interior,
title = {{Interior curvature estimates for convex solutions of a prescribed curvature quotient equation}},
author = {Bin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.20188},
eprint = {2608.20188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20188},
}
RIS
TY - UNPB
TI - Interior curvature estimates for convex solutions of a prescribed curvature quotient equation
AU - Bin Wang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2608.20188
UR - https://arxiv.org/abs/2608.20188
AB - In this note, we prove a priori interior curvature bounds for convex solutions to an elliptic Weingarten curvature quotient equation. The proof avoids integral estimates, doubling inequalities and compactness arguments. It relies on a concavity inequality for the equation operator and a novel choice of the auxiliary function to carry out an elementary maximum-principle argument. As an application, we obtain interior curvature bounds for convex solutions of a prescribed special Lagrangian curvature equation in dimensions three and four.
ER -