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arXiv · 2506.22834

Convolution Regularization Preserves the $L^2$-Estimate Property for $(1,n)$-Forms

Zhuo Liu
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Abstract

In this paper, we prove that the \(L^2\)-estimate property for \((1,n)\)-forms is preserved under the standard convolution regularization. As applications, we show that any singular Hermitian metric satisfying the optimal or multiple coarse \(L^2\)-estimate property for \((n,1)\) or \((1,n)\)-forms is Griffiths semi-positive. This resolves a question posed by Deng--Ning--Wang and a question by Inayama.

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Zhuo Liu. 2026-09-18. Convolution Regularization Preserves the $L^2$-Estimate Property for $(1,n)$-Forms. https://arxiv.org/abs/2506.22834

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