Annales Mathématiques
Blaise Pascal
no. 2
Harmonic functions on Manifolds whose large spheres are small.
Gilles Carron1
1 Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, 2, rue de la Houssinière, B.P. 92208, 44322 Nantes Cedex 3, France
Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 249-261.

On étudie la croissance des fonctions harmoniques sur les variétés riemanniennes complètes dont le diamètre des grandes sphères géodésiques croît sous linéairement. Il s’agit d’une généralisation de travaux de A. Kasue. Nous obtenons aussi un résultat de continuité pour la transformée de Riesz

We study the growth of harmonic functions on complete Riemannian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kasue. Our estimates also yields a result on the boundedness of the Riesz transform.

DOI : 10.5802/ambp.362
Keywords: Poincaré inequality, harmonic function, Riesz transform
Mots clés : Inégalités de Poincaré, fonctions harmoniques, transformée de Riesz.

Gilles Carron 1

1 Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, 2, rue de la Houssinière, B.P. 92208, 44322 Nantes Cedex 3, France 
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Gilles Carron. Harmonic functions on Manifolds whose large spheres are small.. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 249-261. doi : 10.5802/ambp.362. https://ambp.centre-mersenne.org/articles/10.5802/ambp.362/

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