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
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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