Journal of Differential Geometry

Fully non-linear elliptic equations on compact Hermitian manifolds

Gábor Székelyhidi

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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.

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

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

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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.

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