A Liouville theorem on asymptotically Calabi spaces

Song Sun; Ruobing Zhang

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arXiv · 2006.09448

A Liouville theorem on asymptotically Calabi spaces

Song Sun·Ruobing Zhang

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Abstract

In this paper, we will study harmonic functions on the complete and incomplete spaces with nonnegative Ricci curvature which exhibit inhomogeneous collapsing behaviors at infinity. The main result states that any nonconstant harmonic function on such spaces yields a definite exponential growth rate which depends explicitly on the geometric data at infinity.

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Song Sun, Ruobing Zhang. 2020-06-16. A Liouville theorem on asymptotically Calabi spaces. https://arxiv.org/abs/2006.09448

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