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

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 f...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Author: Shih-Kai Chiu
Format: Article
Language:English
Subjects:
Analytic functions
Cones
Harmonic functions
Liouville theorem
Manifolds
Mathematical analysis
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.12965