A Liouville-type Theorem for Smooth Metric Measure Spaces

Details A Liouville-type Theorem for Smooth Metric Measure Spaces A Liouville-type Theorem for Smooth Metric Measure Spaces

2010-06-03

arxiv.org/abs/1006.0751v2

Mathematics

Differential Geometry

7 pages. The proofs are modified to remove the assumption that f is bounded. An example is included demonstrating necessity of

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A Liouville-type Theorem for Smooth Metric Measure Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Liouville-type Theorem for Smooth Metric Measure Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Liouville-type Theorem for Smooth Metric Measure Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-722400