A Liouville-type Theorem for Smooth Metric Measure Spaces

2010/06/03 by Brighton, Kevin · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.0751

Abstract

For smooth metric measure spaces (M, g, e^-f dvol) we prove a Liuoville-type theorem when the Bakry-Emery Ricci tensor is nonnegative. This generalizes a result of Yau, which is recovered in the case f is constant. This result follows from a gradient estimate for f-harmonic functions on smooth metric measure spaces with Bakry-Emery Ricci tensor bounded from below.

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• Gradient estimates and Liouville properties for the drifted Laplacian
• A New proof of Liouville type theorems for a class of semilinear elliptic equations

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