Eigenvalue Comparison on Bakry-Emery Manifolds
By Ben Andrews, Lei Ni. 2011
68 citations recorded by the source corpus.
We prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof of an eigenvalue comparison result of Bakry-Qian. Examples are given to show that the estimate is sharp. Discussions on an explicit lower estimate for the corresponding ODE and an application to the diameter lower bound for gradient shrinking solitons are also included.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9dbdbe77113f686672f441b781947a6f4822bc16
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In Applied Mathematics
- Xu Cheng
- Ben Andrews
- Detang Zhou
- Julie Clutterbuck
- Robert Haslhofer
- James A. McCoy
- S. Brendle
- Bruce Kleiner
In Geometry and Topology
- Xu Cheng
- Detang Zhou
- Ben Andrews
- Robert Haslhofer
- S. Brendle
- Bruce Kleiner
- James A. McCoy
- T. Colding
Citations in the corpus
- Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue (2012, background): “A similar argument proving the sharp lower bound for λ1 on a Bakry–Emery manifold may be found in [Andrews and Ni 2012].”
- Eigenvalues of the drifted Laplacian on complete metric measure spaces (2013, background): “The authors of [2] stated, by constructing examples, that their estimates are sharp when Bakry-Émery Ricci tensor is not constant (see details in [8], [2] and [7]).”