scholarly journals Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds

1997 ◽  
Vol 179 (1) ◽  
pp. 79-103 ◽  
Author(s):  
James R. Norris
Keyword(s):  
Heat Kernel ◽  
Distance Function ◽  
Riemannian Manifolds ◽  
Heat Kernel Asymptotics

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.

Embedding Riemannian manifolds by their heat kernel

1994 ◽  
Vol 4 (4) ◽  
pp. 373-398 ◽  
Author(s):  
P. Bérard ◽  
G. Besson ◽  
S. Gallot
Keyword(s):  
Heat Kernel ◽  
Riemannian Manifolds
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