Weak solutions of complex Hessian equations on compact Hermitian manifolds

Abstract

We prove the existence of weak solutions of complex $m-$Hessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to $L^p,p>n/m$ ($n$ is the dimension of the manifold). For smooth, positive data the equation has been recently solved by Szekelyhidi and Zhang. We also give a stability result for such solutions.

27 pages, accepted by Compos. Math

References in corpus (3)

• Pluripotential estimates on compact Hermitian manifolds
• On estimates for the Fu-Yau generalization of a Strominger system
• On uniform estimate of complex elliptic equations on closed Hermitian manifolds

Cited by in corpus (9)

• The Fu-Yau equation with negative slope parameter
• On estimates for the Fu-Yau generalization of a Strominger system
• On the Hölder continuous subsolution problem for the complex Monge-Ampère equation, II
• Fully non-linear degenerate elliptic equations in complex geometry
• Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
• Complex Hessian measures with respect to a background Hermitian form
• A second order estimate for general complex Hessian equations
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds
• The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary