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Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications.
- Source :
-
Journal of Geometry & Physics . Dec2023, Vol. 194, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- We establish a Gaussian upper bound of the heat kernel for the Laplace-Beltrami operator on complete Riemannian manifolds with Bakry-Émery Ricci curvature bounded below. As applications, we first prove an L 1 -Liouville property for non-negative subharmonic functions when the potential function of the Bakry-Émery Ricci curvature tensor is of at most quadratic growth. Then we derive lower bounds of the eigenvalues of the Laplace-Beltrami operator on closed manifolds. An upper bound of the bottom spectrum is also obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 194
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 174031867
- Full Text :
- https://doi.org/10.1016/j.geomphys.2023.104997