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arXiv · 2410.15014

On the residual Monge-Amp\`{e}re mass of plurisubharmonic functions, III: uniformly directional Lipschitz

Weiyong He·Long Li·Xiaowei Xu
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Abstract

The purpose of this article is to study the (residual) Monge-Amp\`{e}re mass of a plurisubharmonic function with an isolated unbounded locus. A general decomposition formula is obtained under the Sasakian structure of the unit sphere. In complex dimension two, we obtain an $L^{1}$-apriori estimate on the complex Monge-Amp\`{e}re operator. This induces an upper-bound estimate on the residual mass, provided with the uniform directional Lipschitz continuity. As an application, the zero mass conjecture is confirmed, if the function further separates the circular direction in its alternating part.

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Weiyong He, Long Li, Xiaowei Xu. 2024-10-19. On the residual Monge-Amp\`{e}re mass of plurisubharmonic functions, III: uniformly directional Lipschitz. https://arxiv.org/abs/2410.15014

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