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arXiv · 2510.14690

Continuity of solutions to complex Hessian equations on compact Hermitian manifolds

Yuetong Fang
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Abstract

Let $(X,ω)$ be a compact Hermitian manifold of dimension $n$. We derive an $L^\infty$-estimate for bounded solutions to the complex $m$-th Hessian equations on $X$, assuming a positive right-hand side in the Orlicz space $L^{\frac{n}{m}}(\log L)^n(h\circ\log \circ \log L)^n$, where the associated weight satisfies Kołodziej's Condition. Building upon this estimate, we then establish the existence of continuous solutions to the complex Hessian equation under the prescribed assumptions.

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Yuetong Fang. 2025-10-16. Continuity of solutions to complex Hessian equations on compact Hermitian manifolds. https://arxiv.org/abs/2510.14690

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