Baptiste Devyver
Published 2018-03-27, updated 2018-04-11Version 2
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.
Comments: 62 pages, more detailed introduction
The heat kernel on an asymptotically conic manifold
On Davies' conjecture and strong ratio limit properties for the heat kernel
An $\infty$-Laplacian for differential forms, and calibrated laminations
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