Viscosity solution to complex Hessian quotient equations

Jingrui Cheng; Yulun Xu

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arXiv · 2501.17016

Viscosity solution to complex Hessian quotient equations

Jingrui Cheng·Yulun Xu

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Abstract

In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the viscosity sense. The results cover the complex Hessian quotient equations. This generalized our previous results where the equation needs to satisfy a determinant domination condition.

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Jingrui Cheng, Yulun Xu. 2025-01-28. Viscosity solution to complex Hessian quotient equations. https://arxiv.org/abs/2501.17016

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