9d42b784d21051c34a0e329db99ff017 AIF.StableNormsNonOrientableSurfaces.pdf 867ea782886f8e271190fd88d7303f1531715a40 AIF.StableNormsNonOrientableSurfaces.pdf c0904d692d5eb768a453d53c052ade91c4fbca2d389d7b328826dbb17bd7bb1e AIF.StableNormsNonOrientableSurfaces.pdf Title: Stable norms of non-orientable surfaces Subject: © Association des Annales de l'institut Fourier Keywords: Produit dans le cadre du CEDRAM, http://www.cedram.org/ Author: Florent Balacheff& Daniel Massart Creator: NUMDAM Producer: pdfeTeX-1.305 CreationDate: Mon May 5 09:46:18 2008 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 34 Encrypted: no Page size: 447.874 x 680.315 pts Page rot: 0 File size: 1132242 bytes Optimized: yes PDF version: 1.4 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- NMHAXA+LMSans10-Regular Type 1 Custom yes yes no 580 0 YVVEDL+LMSans9-Regular Type 1 Custom yes yes no 588 0 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2024-02-01 02:45:24 CET RepresentationInformation: AIF.StableNormsNonOrientableSurfaces.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2024-01-31 12:11:51 CET Size: 1132242 Format: PDF Version: 1.4 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf Profile: Linearized PDF PDFMetadata: Objects: 691 FreeObjects: 1 IncrementalUpdates: 1 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseOutlines Outlines: Item: Title: 1.Introduction Item: Title: 2.Preliminaries: non-orientable surfaces Children: Item: Title: 2.1.First homology group Item: Title: 2.2.Orientation cover Item: Title: 3.Preliminaries: minimizing measures and stable norm Children: Item: Title: 3.1.Minimizing measures Item: Title: 3.2.Link with Mather's theory Item: Title: 4.Flats of the unit ball Item: Title: 5.Technical lemmas Children: Item: Title: 5.1.Key lemma, one-sided case Children: Item: Title: 5.1.1.First case Item: Title: 5.1.2.Second case Item: Title: 5.1.3.Third case Item: Title: 5.2.Key lemma, two-sided case Children: Item: Title: 5.2.1.First case Item: Title: 5.2.2.Second case Item: Title: 5.2.3.Third case Item: Title: 5.3.Consequences of the key lemmas Item: Title: 5.4.Geodesics asymptotic to closed geodesics Item: Title: 5.5.Minimizing measures with rational homology classes Item: Title: 6.Proofs of the main theorems Children: Item: Title: 6.1.Local results - Orientable case Item: Title: 6.2.Local results - Non-orientable case Item: Title: 6.3.Global result - Proof of Theorem 1.3 Item: Title: Bibliography Info: Title: Stable norms of non-orientable surfaces Author: Florent Balacheff& Daniel Massart Subject: © Association des Annales de l'institut Fourier Keywords: Produit dans le cadre du 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