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Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth
Communications on Pure and Applied Mathematics ( IF 3.1 ) Pub Date : 2023-11-16 , DOI: 10.1002/cpa.22182
Shih‐Kai Chiu 1
Affiliation  

On a complete Calabi-Yau manifold M $M$ 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 $L^2$ estimate of the exterior derivative.

中文翻译:

具有最大体积增长的 Calabi-Yau 流形上的次二次调和函数

在完整的 Calabi-Yau 流形上 中号 $M$ 在最大体积增长的情况下,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-形式的刘维尔型定理来证明这个结果,该定理源自一个新的局部 L 2 $L^2$ 外导数的估计。
更新日期:2023-11-16
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