Viscosity solution to complex Hessian equations on compact Hermitian manifolds

Jingrui Cheng; Yulun Xu

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arXiv · 2406.00953

Viscosity solution to complex Hessian equations on compact Hermitian manifolds

Jingrui Cheng·Yulun Xu

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Abstract

We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant.

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Jingrui Cheng, Yulun Xu. 2024-06-03. Viscosity solution to complex Hessian equations on compact Hermitian manifolds. https://arxiv.org/abs/2406.00953

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