An ℓ 1 -norm-mass inequality for complete manifolds
[Une inégalité entre norme ℓ 1 et masse pour les variétés complètes]
Campagnolo, Caterina1 ; Wang, Shi2
1 Universidad Autónoma de Madrid Departamento de Matemáticas C/ Nicolás Cabrera, 13-15 28049 Madrid (Spain)
2 ShanghaiTech University Institute of Mathematical Sciences Pudong, Shanghai (China)
Annales de l'Institut Fourier, Online first, 22 p.

Nous généralisons une inégalité de Besson–Courtois–Gallot entre le volume et le volume simplicial des variétés fermées à la norme ℓ 1 de toutes les classes d’homologie des variétés complètes. L’inégalité s’exprime en termes de l’exposant critique du groupe fondamental de la variété et de la masse des classes d’homologie.

We generalize an inequality of Besson–Courtois–Gallot about volume and simplicial volume of closed manifolds to the ℓ 1 -norm of all the homology classes of complete manifolds. The inequality involves the critical exponent of the fundamental group of the manifold and the mass of the homology classes.

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DOI : 10.5802/aif.3643
Classification : 53C23, 57R57
Keywords: Gromov norm, critical exponent, mass, comass, complete manifold.
Mot clés : norme de Gromov, exposant critique, masse, comasse, variété complète.
Campagnolo, Caterina 1 ; Wang, Shi 2

1 Universidad Autónoma de Madrid Departamento de Matemáticas C/ Nicolás Cabrera, 13-15 28049 Madrid (Spain)
2 ShanghaiTech University Institute of Mathematical Sciences Pudong, Shanghai (China) 
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Campagnolo, Caterina; Wang, Shi. An $\ell _1$-norm-mass inequality for complete manifolds. Annales de l'Institut Fourier, Online first, 22 p.

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