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Volumes and areas of lipschitz metrics. / Ivanov, S. V.

In: St. Petersburg Mathematical Journal, Vol. 20, No. 3, 01.01.2009, p. 381-405.

Research output: Contribution to journal › Article › peer-review

Harvard

Ivanov, SV 2009, 'Volumes and areas of lipschitz metrics', St. Petersburg Mathematical Journal, vol. 20, no. 3, pp. 381-405. https://doi.org/10.1090/S1061-0022-09-01053-X

APA

Ivanov, S. V. (2009). Volumes and areas of lipschitz metrics. St. Petersburg Mathematical Journal, 20(3), 381-405. https://doi.org/10.1090/S1061-0022-09-01053-X

Vancouver

Ivanov SV. Volumes and areas of lipschitz metrics. St. Petersburg Mathematical Journal. 2009 Jan 1;20(3):381-405. https://doi.org/10.1090/S1061-0022-09-01053-X

Author

Ivanov, S. V. / Volumes and areas of lipschitz metrics. In: St. Petersburg Mathematical Journal. 2009 ; Vol. 20, No. 3. pp. 381-405.

BibTeX

@article{1a690f638639428abb6e27a6f92f4169,
title = "Volumes and areas of lipschitz metrics",
abstract = "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.",
keywords = "(strong) geodesic minimality property, Filling volume, Finsler volume functional",
author = "Ivanov, {S. V.}",
year = "2009",
month = jan,
day = "1",
doi = "10.1090/S1061-0022-09-01053-X",
language = "English",
volume = "20",
pages = "381--405",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Volumes and areas of lipschitz metrics

AU - Ivanov, S. V.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

KW - (strong) geodesic minimality property

KW - Filling volume

KW - Finsler volume functional

UR - http://www.scopus.com/inward/record.url?scp=85009804206&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-09-01053-X

DO - 10.1090/S1061-0022-09-01053-X

M3 - Article

AN - SCOPUS:85009804206

VL - 20

SP - 381

EP - 405

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 3

ER -

ID: 49984630