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arXiv · 1905.12965

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

Shih-Kai Chiu
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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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Shih-Kai Chiu. 2019-05-30. Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth. https://doi.org/10.1002/cpa.22182

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