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Off‐Diagonal Heat Kernel Lower Bounds Without Poincaré
Author(s) -
Coulhon Thierry
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004770
Subject(s) - heat kernel , mathematics , gaussian , upper and lower bounds , diagonal , characterization (materials science) , kernel (algebra) , poincaré inequality , simple (philosophy) , matching (statistics) , sobolev inequality , poincaré conjecture , combinatorics , sobolev space , mathematical analysis , inequality , physics , geometry , statistics , philosophy , epistemology , quantum mechanics , optics
On a manifold with polynomial volume growth satisfying Gaussian upper bounds of the heat kernel, a simple characterization of the matching lower bounds is given in terms of a certain Sobolev inequality. The method also works in the case of so‐called sub‐Gaussian or sub‐diffusive heat kernels estimates, which are typical of fractals. Together with previously known results, this yields a new characterization of the full upper and lower Gaussian or sub‐Gaussian heat kernel estimates.