Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-11-16 DOI:10.1002/cpa.22182

Shih-Kai Chiu

引用次数: 0

Abstract

On a complete Calabi-Yau manifold $M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville-type theorem for harmonic 1-forms, which follows from a new local $L^{2}$ estimate of the exterior derivative.

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最大体积增长的Calabi-Yau流形上的次二次调和函数

在具有极大体积增长的完全Calabi-Yau流形M上，具有次二次多项式增长的调和函数是全纯函数的实部。这概括了Conlon-Hein的结果。我们通过证明调和1型的liouville型定理来证明这一结果，该定理由外导数的一个新的局部L2估计推导而来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.