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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

[1]Ambrosio, L., Fusco, N. and Pallara, D., Functions of bounded variation and free discontinuous problems, Oxford Mathematical Monographs (The Clarendon Press Oxford University Press, New York, 2000).Google Scholar
[2]Bakry, D., ‘Études des transformations de Rienz dans les variétés riemanniennes à courbure de Ricci minorée’, Lecture Notes in Maths 1247 (Springer-Verlag, Verlin).Google Scholar
[3]De Giorgi, E., ‘Su una teoria generale della misura (r − 1)-dimensionale in uno spazio ad r dimensioni’, Ann. Mat. Pura Appl. 36 (1954), 191–213.Google Scholar
[4]De Giorgi, E., Selected Papers, (Ambrosio, L., Maso, G. Dal, Forti, M., Miranda, M., Spagnolo, S., Editors) (Springer Verlag, Berlin, Heidelberg, 2006).Google Scholar
[5]Fichera, G., Lezioni sulle trasformazioni lineari, Istituto Matematico dell'Università di Trieste, Vol. I, 1954.Google Scholar
[6]Miranda, M., ‘Distribuzioni aventi derivate misure. Insiemi di perimetro localmente finito’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964), 27–56.Google Scholar
[7]Miranda, M. Jr., Pallara, D., Paronetto, F. and Preunkert, M., ‘Heat semigroup and functions of bounded variation on Riemannian manifolds’, (preprint (2005) cvgmt.sns.it/papers/mirpalpar05a/).Google Scholar
[8]Strichartz, R.S., ‘Analysis of the Laplacian on the complete Riemannian manifold’, J. Funct. Anal. 52 (1983), 48–79.CrossRefGoogle Scholar
[9]Shubin, M., ‘Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds’, J. Funct. Anal. 186 (2001), 92–116.Google Scholar