Journal of Differential Geometry

Fully non-linear elliptic equations on compact Hermitian manifolds

Gábor Székelyhidi

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Abstract

We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge–Ampère, Hessian and inverse Hessian equations. As an application we solve a class of Hessian quotient equations on Kähler manifolds assuming the existence of a suitable subsolution. The method also applies to analogous equations on compact Riemannian manifolds.

Article information

Source
J. Differential Geom., Volume 109, Number 2 (2018), 337-378.

Dates
Received: 23 February 2016
First available in Project Euclid: 23 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1527040875

Digital Object Identifier
doi:10.4310/jdg/1527040875

Mathematical Reviews number (MathSciNet)
MR3807322

Zentralblatt MATH identifier
06877022

Citation

Székelyhidi, Gábor. Fully non-linear elliptic equations on compact Hermitian manifolds. J. Differential Geom. 109 (2018), no. 2, 337--378. doi:10.4310/jdg/1527040875. https://projecteuclid.org/euclid.jdg/1527040875


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