Hessian estimates for convex solutions to quadratic Hessian equation
Matt McGonagle, Chong Song, Yu Yuan
TL;DR
This paper develops Hessian estimates for convex solutions to quadratic Hessian equations using a compactness argument, advancing understanding of these nonlinear PDEs.
Contribution
It introduces a novel approach to estimate the Hessian of convex solutions to quadratic Hessian equations.
Findings
Hessian estimates are established for convex solutions
The method relies on a compactness argument
Results improve existing bounds for solutions
Abstract
We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations