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Introduction Children: Item: Title: 1.1. Finsler metrics Item: Title: 1.2. Systole and Finsler areas Item: Title: 1.3. Optimal isosystolic inequalities Item: Title: 1.4. Organization of the paper Item: Title: 2. Isosystolic inequalities for flat and non-flat Riemannian metrics Children: Item: Title: 2.1. The flat Riemannian case: Hermite constant in dimension 2 Item: Title: 2.2. The Riemannian case: Loewner's isosystolic inequality Item: Title: 3. Isosystolic inequalities for flat Finsler metrics Children: Item: Title: 3.1. Busemann Hausdorff area in the flat reversible case Item: Title: 3.2. Busemann Hausdorff area in the flat non-reversible case: Systolic freedom Item: Title: 3.3. Holmes Thompson area in the flat reversible case Item: Title: 3.4. Holmes Thompson area in the flat non-reversible case Item: Title: 4. Asymptotic geometry in the universal cover of a Finsler 2-torus Children: Item: Title: 4.1. Stable norm Item: Title: 4.2. Dual stable norm and calibrating functions Item: Title: 5. Isosystolic inequalities for Finsler metrics and Holmes Thompson area Children: Item: Title: 5.1. Decreasing the Holmes Thompson area Item: Title: 5.2. Holmes Thompson area in the non-flat reversible case Item: Title: 5.3. Holmes Thompson area in the non-flat and non-reversible case Item: Title: 6. Isosystolic inequality for reversible Finsler metrics and Busemann Hausdorff area Children: Item: Title: 6.1. Decreasing the Busemann Hausdorff area Item: Title: 6.2. A counterexample in the non-reversible case Item: Title: References Info: Title: Author: Subject: Keywords: Creator: LaTeX with hyperref Producer: pdfTeX-1.40.26 CreationDate: Wed Sep 25 11:41:05 CEST 2024 ModDate: Wed Sep 25 11:41:05 CEST 2024 ID: 0x78fedcf4411cd5589de3bb16301b48ed, 0x78fedcf4411cd5589de3bb16301b48ed Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: ICDQMZ+NimbusRomNo9L-Regu FontSubset: true FirstChar: 2 LastChar: 252 FontDescriptor: FontName: ICDQMZ+NimbusRomNo9L-Regu Flags: Symbolic FontBBox: -168, -281, 1000, 924 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: HKWQVW+MT2MSS FontSubset: true FirstChar: 9 LastChar: 9 FontDescriptor: FontName: HKWQVW+MT2MSS Flags: Symbolic FontBBox: 0, -189, 1103, 750 FontFile: true ToUnicode: true Font: BaseFont: SRCHUZ+NimbusRomNo9L-Medi FontSubset: true FirstChar: 2 LastChar: 150 FontDescriptor: FontName: SRCHUZ+NimbusRomNo9L-Medi Flags: Symbolic FontBBox: -168, -341, 1000, 960 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