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A note on bounded variation and heat semigroup on Riemannian manifolds

Published online by Cambridge University Press:  17 April 2009

A. Carbonaro  and
G. Mauceri
A. Carbonaro
Affiliation:
Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
G. Mauceri
Affiliation:
Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 155 - 160
Copyright
Copyright © Australian Mathematical Society 2007

References

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