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arXiv · 2010.03431

Fully non-linear degenerate elliptic equations in complex geometry

Jianchun Chu·Nicholas McCleerey
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Abstract

We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This improves on the estimates of Sz\'ekelyhidi and additionally applies to elliptic equations with a degenerate right-hand side. As an application, we establish the optimal $C^{1,1}$ regularity of envelopes of $(\theta, m)$-subharmonic functions on compact Hermitian manifolds.

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Jianchun Chu, Nicholas McCleerey. 2020-10-07. Fully non-linear degenerate elliptic equations in complex geometry. https://arxiv.org/abs/2010.03431

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