Stable norms of non-orientable surfaces

Florent Balacheff; Daniel Massart

doi:10.5802/aif.2386

Stable norms of non-orientable surfaces

Florent Balacheff^*, Daniel Massart

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.

Original language	English
Pages (from-to)	1337-1369
Number of pages	33
Journal	Annales de l'Institut Fourier
Volume	58
Issue number	4
DOIs	https://doi.org/10.5802/aif.2386
Publication status	Published - 2008

Keywords

Minimizing measures
non-orientable surface
stable norm

Access to Document

10.5802/aif.2386

Cite this

@article{5569cd96adf2400692f80fdd29980a78,

title = "Stable norms of non-orientable surfaces",

abstract = "We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.",

keywords = "Minimizing measures, non-orientable surface, stable norm",

author = "Florent Balacheff and Daniel Massart",

year = "2008",

doi = "10.5802/aif.2386",

language = "English",

volume = "58",

pages = "1337--1369",

journal = "Annales de l'Institut Fourier",

issn = "0373-0956",

publisher = "Association des Annales de l'Institut Fourier",

number = "4",

}

TY - JOUR

T1 - Stable norms of non-orientable surfaces

AU - Balacheff, Florent

AU - Massart, Daniel

PY - 2008

Y1 - 2008

N2 - We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.

AB - We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.

KW - Minimizing measures

KW - non-orientable surface

KW - stable norm

UR - http://www.scopus.com/inward/record.url?scp=47649088509&partnerID=8YFLogxK

U2 - 10.5802/aif.2386

DO - 10.5802/aif.2386

M3 - Article

AN - SCOPUS:47649088509

SN - 0373-0956

VL - 58

SP - 1337

EP - 1369

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 4

ER -

Stable norms of non-orientable surfaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this