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Generalized Li-Yau estimates and Huisken's monotonicity formula
- Publication Year :
- 2012
-
Abstract
- We prove a generalization of the Li-Yau estimate for a board class of second order linear parabolic equations. As a consequence, we obtain a new Cheeger-Yau inequality and a new Harnack inequality for these equations. We also prove a Hamilton-Li-Yau estimate, which is a matrix version of the Li-Yau estimate, for these equations. This results in a generalization of Huisken's monotonicity formula for a family of evolving hypersurfaces. Finally, we also show that all these generalizations are sharp in the sense that the inequalities become equalities for a family of fundamental solutions, which however different from the Gaussian heat kernels on which the equality was achieved in the classical case.<br />Comment: 31 pages
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
58J35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1211.5559
- Document Type :
- Working Paper