A Liouville-Type Theorem for Smooth Metric Measure Spaces

By Kevin Brighton. 2010

101 citations recorded by the source corpus.

For smooth metric measure spaces (M,g,e−fdvol) we prove a Liouville-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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5cd3753ec35c8af42c6d46b3a69b78a16648f762

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In Applied Mathematics

1. Ovidiu Munteanu
2. Jiaping Wang
3. G. Carron
4. Jia-Yong Wu

In Geometry and Topology

1. Ovidiu Munteanu
2. Jiaping Wang
3. G. Carron
4. Jia-Yong Wu

Citations in the corpus

• Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature (2014, unknown): “11, we generalize a result in [7,24] about the Liouville theorem.”
• Smooth metric measure spaces with non-negative curvature (2011, methodology): “th only the growth assumption on f,this direct approach seems to run into essential obstacles. Our argument relies on both Yau’s idea and the well known De Giorgi-Nash-Moser theory. In a recent paper [2], Brighton, by applying Yau’s idea to function uǫ instead of logu,proved bounded f-harmonic funct”