BibTex format
@article{Li:2022,
author = {Li, X-M and Chen, X and Wu, B},
journal = {Annals of Probability},
title = {LOGARITHMIC HEAT KERNEL ESTIMATES WITHOUT CURVATURE RESTRICTIONS},
year = {2022}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - JOUR
AB - The main results of the article are short time estimates and asymptotic estimates for the first two order derivatives of the logarithmic heat kernel of a complete Riemannian manifold. We remove all curvature restrictions and also develop several techniques.A basic tool developed here is intrinsic stochastic variations with pre- scribed second order covariant differentials, allowing to obtain a path inte- gration representation for the second order derivatives of the heat semigroup Pt on a complete Riemannian manifold, again without any assumptions on the curvature. The novelty is the introduction of an ε2 term in the variation allowing greater control. We also construct a family of cut-off stochastic pro- cesses adapted to an exhaustion by compact subsets with smooth boundaries, each process is constructed path by path and differentiable in time, further- more the differentials have locally uniformly bounded moments with respect to the Brownian motion measures, allowing to by-pass the lack of continuity of the exit time of the Brownian motions on its initial position.
AU - Li,X-M
AU - Chen,X
AU - Wu,B
PY - 2022///
SN - 0091-1798
TI - LOGARITHMIC HEAT KERNEL ESTIMATES WITHOUT CURVATURE RESTRICTIONS
T2 - Annals of Probability
ER -