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arXiv · 2610.06719

Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds

Yuetong Fang
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Abstract

We establish an a priori $C^2$-estimate for complex Hessian equations on compact Hermitian manifolds. As an application, we obtain a regularity result for solutions to complex Hessian equation with densities of the right hand side depending on the solution. This generalizes Székelyhidi--Tosatti's result to the setting of complex Hessian equations on Hermitian manifolds.

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Yuetong Fang. 2026-10-05. Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds. https://arxiv.org/abs/2610.06719

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