Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding maps to Banach spaces of L∞-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∞-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.
Original language | English |
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Pages (from-to) | 381-405 |
Number of pages | 25 |
Journal | St. Petersburg Mathematical Journal |
Volume | 20 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2009 |
Externally published | Yes |
ID: 49984630