A Liouville theorem on asymptotically Calabi spaces

Song Sun; Ruobing Zhang

doi:10.1007/s00526-021-01949-z

A Liouville theorem on asymptotically Calabi spaces

Song Sun, Ruobing Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Article number	103
Journal	Calculus of Variations and Partial Differential Equations
Volume	60
Issue number	3
DOIs	https://doi.org/10.1007/s00526-021-01949-z
State	Published - Jun 2021

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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title = "A Liouville theorem on asymptotically Calabi spaces",

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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A Liouville theorem on asymptotically Calabi spaces

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