scholarly journals Gaussian heat kernel estimates: From functions to forms

2020 ◽  
Vol 2020 (761) ◽  
pp. 25-79
Author(s):  
Thierry Coulhon ◽  
Baptiste Devyver ◽  
Adam Sikora
Keyword(s):  
Riemannian Manifold ◽  
Heat Kernel ◽  
Ricci Curvature ◽  
Compact Riemannian Manifold ◽  
Kernel Estimates ◽  
Doubling Property ◽  
Negative Part ◽  
Heat Kernel Estimates ◽  
Volume Doubling ◽  
Upper Estimate

AbstractOn a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic 1-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity.

Gradient estimates and heat kernel estimates

1995 ◽  
Vol 125 (5) ◽  
pp. 975-990 ◽  
Author(s):  
Zhongmin Qian
Keyword(s):  
Riemannian Manifold ◽  
Differential Operator ◽  
Heat Kernel ◽  
Harmonic Functions ◽  
Complete Riemannian Manifold ◽  
Gradient Estimates ◽  
Order Differential Operator ◽  
Kernel Estimates ◽  
Heat Kernel Estimates ◽  
Girsanov’S Formula

In the first part of this paper, Yau's estimates for positive L-harmonic functions and Li and Yau's gradient estimates for the positive solutions of a general parabolic heat equation on a complete Riemannian manifold are obtained by the use of Bakry and Emery's theory. In the second part we establish a heat kernel bound for a second-order differential operator which has a bounded and measurable drift, using Girsanov's formula.

scholarly journals Stability of heat kernel estimates for symmetric non-local Dirichlet forms

2021 ◽  
Vol 271 (1330) ◽  
Author(s):  
Zhen-Qing Chen ◽  
Takashi Kumagai ◽  
Jian Wang
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Metric Measure Spaces ◽  
Kernel Estimates ◽  
Open Problems ◽  
Content Type ◽  
Heat Kernel Estimates ◽  
Measure Spaces ◽  
Non Local ◽  
Volume Doubling

In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for α \alpha -stable-like processes even with α ≥ 2 \alpha \ge 2 when the underlying spaces have walk dimensions larger than 2 2 , which has been one of the major open problems in this area.

Two-sided heat kernel estimates for censored stable-like processes

2009 ◽  
Vol 146 (3-4) ◽  
pp. 361-399 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Panki Kim ◽  
Renming Song
Keyword(s):  
Heat Kernel ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

Heat Kernel Estimates on Weighted Graphs

2000 ◽  
Vol 32 (4) ◽  
pp. 477-483 ◽  
Author(s):  
Bernd Metzger ◽  
Peter Stollmann
Keyword(s):  
Heat Kernel ◽  
Weighted Graphs ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

scholarly journals Sharp Two-Sided Heat Kernel Estimates of Twisted Tubes and Applications

2014 ◽  
Vol 213 (1) ◽  
pp. 215-243 ◽  
Author(s):  
Gabriele Grillo ◽  
Hynek Kovařík ◽  
Yehuda Pinchover
Keyword(s):  
Heat Kernel ◽  
Kernel Estimates ◽  
Heat Kernel Estimates ◽  
Twisted Tubes
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