Liouville-type theorems and applications to geometry on complete\n Riemannian manifolds

2010/11/06 by Chanyoung Sung, Sung, Chanyoung · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1011.1540

Abstract

On a complete Riemannian manifold M with Ricci curvature satisfying\n
textrmRic(
nabla r,
nabla r)
geq -Ar²(
log r)²(
log(
log\nr))²...(
log^kr)² for r\≫ 1, where A>0 is a constant, and r is the\ndistance from an arbitrarily fixed point in M. we prove some Liouville-type\ntheorems for a C² function f:M\→ Bbb R satisfying \Δ f\≥\nF(f) for a function F: Bbb R\→ Bbb R.\n

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