Geodesic
Volumes and areas of Lipschitz metrics
Algebra i analiz, Tome 20 (2008) no. 3, pp. 74-111.

Voir la notice de l'article provenant de la source Math-Net.Ru

Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding maps to Banach spaces of $L^\infty$ type are developed and generalized. For every Finsler volume functional (such as the Busemann volume or the Holmes–Thompson volume), a natural extension is constructed from the class of Finsler metrics to all Lipschitz metrics, and the notion of area is defined for Lipschitz surfaces in a Banach space. A correspondence is established between minimal fillings and minimal surfaces in $L^\infty$ type spaces. A Finsler volume functional for which the Riemannian and the Finsler filling volumes are equal is introduced; it is proved that this functional is semielliptic.
Keywords: Filling volume, Finsler volume functional, (strong) geodesic minimality property. 
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S. V. Ivanov. Volumes and areas of Lipschitz metrics. Algebra i analiz, Tome 20 (2008) no. 3, pp. 74-111. http://geodesic.mathdoc.fr/item/AA_2008_20_3_a3/

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