On gradient estimates for the heat kernel
Abstract
We study pointwise and $L^p$ gradient estimates of the heat kernel, on manifolds that may have some amount of negative Ricci curvature, provided it is not too negative (in an integral sense) at infinity. We also prove uniform boundedness results on $L^p$ spaces for the heat operator of the Hodge Laplacian on differential forms.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2018
- DOI:
- arXiv:
- arXiv:1803.10015
- Bibcode:
- 2018arXiv180310015D
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Differential Geometry;
- 35K08;
- 58J35
- E-Print:
- 67 pages, a mistake in the proof of Corollary 1.9 has been corrected