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A Liouville theorem on asymptotically Calabi spaces. (English) Zbl 1467.53067

Summary: 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.

MSC:

53C43 Differential geometric aspects of harmonic maps
35R01 PDEs on manifolds
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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References:

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