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arXiv · 2208.14539

Regularization Of $m$-subharmonic Functions And H\"Older Continuity

Jingrui Cheng·Yulun Xu
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Abstract

We use sup-convolution to find upper approximations of a bounded $m$-subharmonic function on a compact K\"ahler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the H\"older continuity of solutions to $\sigma_m$ equation when the right hand side is in $L^p$, $p>\frac{n}{m}$. All these results generalize to more general complex Hessian equations.

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Jingrui Cheng, Yulun Xu. 2022-08-30. Regularization Of $m$-subharmonic Functions And H\"Older Continuity. https://arxiv.org/abs/2208.14539

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