A Gaussian Lower Bound for the Dirichlet Heat Kernel

1992 ◽  
Vol 24 (5) ◽  
pp. 475-477 ◽  
Author(s):  
M. van den Berg
Keyword(s):  
Lower Bound ◽  
Heat Kernel ◽  
Dirichlet Heat Kernel

Heat equation and the principle of not feeling the boundary

1989 ◽  
Vol 112 (3-4) ◽  
pp. 257-262 ◽  
Author(s):  
M. van den Berg
Keyword(s):  
Lower Bound ◽  
Heat Equation ◽  
Heat Kernel ◽  
Open Set ◽  
Dirichlet Heat Kernel

SynopsisWe prove a lower bound for the Dirichlet heat kernel pD(x,y;t), where x and y are a visible pair of points in an open set D in ℝm.

scholarly journals A note on bounded variation and heat semigroup on Riemannian manifolds

2007 ◽  
Vol 76 (1) ◽  
pp. 155-160 ◽  
Author(s):  
A. Carbonaro ◽  
G. Mauceri
Keyword(s):  
Lower Bound ◽  
Euclidean Space ◽  
Heat Kernel ◽  
Ricci Curvature ◽  
Bounded Variation ◽  
Riemannian Manifolds ◽  
Heat Semigroup ◽  
Functions Of Bounded Variation ◽  
Fixed Radius ◽  
Lower Bound Estimate

In a recent paper Miranda Jr., Pallara, Paronetto and Preunkert have shown that the classical De Giorgi's heat kernel characterisation of functions of bounded variation on Euclidean space extends to Riemannian manifolds with Ricci curvature bounded from below and which satisfy a uniform lower bound estimate on the volume of geodesic balls of fixed radius. We give a shorter proof of the same result assuming only the lower bound on the Ricci curvature.

Heat kernel estimates and lower bound of eigenvalues

1981 ◽  
Vol 56 (1) ◽  
pp. 327-338 ◽  
Author(s):  
Shiu-Yuen Cheng ◽  
Peter Li
Keyword(s):  
Lower Bound ◽  
Heat Kernel ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

A lower bound for the heat kernel

1981 ◽  
Vol 34 (4) ◽  
pp. 465-480 ◽  
Author(s):  
Jeff Cheeger ◽  
Shing-Tung Yau
Keyword(s):  
Lower Bound ◽  
Heat Kernel
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