A gradient estimate for the Hermitian Monge-Amp\`ere equation
Abdellah Hanani
TL;DR
This paper improves gradient and second order derivative estimates for the Hermitian Monge-Ampère equation on compact manifolds, facilitating advanced regularity results for solutions.
Contribution
It provides new gradient and second order derivative estimates for the Hermitian Monge-Ampère equation, extending previous results and enabling application of Evans-Krylov and third derivative estimates.
Findings
Enhanced gradient estimates for the Hermitian Monge-Ampère equation
Derived second order derivative estimates including non-mixed derivatives
Facilitated application of Evans-Krylov and third derivative estimates
Abstract
We improve our previous gradient estimate for the Monge-Amp\`ere equation on a compact Hermitian manifold and give a estimates for the non-mixed second order derivatives. These estimates are required to apply either the Evans-Krylov estimates for second order derivatives or the third derivatives estimates for equations with a gradient term.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics