Fully non-linear degenerate elliptic equations in complex geometry

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 Székelyhidi 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.

arXiv comment40 pages; small changes, final version to appear in Journal of Functional Analysis

References in corpus (5)

• The Space of Kähler metrics (II)
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• Form-type Calabi-Yau equations on Kähler manifolds of nonnegative orthogonal bisectional curvature

Cited by in corpus (2)

• Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Ampère volumes
• Fully non-linear elliptic equations on compact almost Hermitian manifolds