scholarly journals EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL

2012 ◽  
Vol 49 (5) ◽  
pp. 939-947 ◽  
Author(s):  
Hiba Abdalla
Keyword(s):  
Heat Kernel ◽  
Riemannian Manifolds

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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