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SinglePage PageMode: UseOutlines Language: en Outlines: Item: Title: The Santaló point for the Holmes-Thompson boundary area Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612fc6eb Children: Item: Title: 1 Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1060b431 Children: Item: Title: Acknowledgments Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612679d6 Item: Title: 2 Background on the Holmes-Thompson notions of volume and area Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@11758f2a Children: Item: Title: 2.1 Holmes-Thompson volume on continuous Finsler manifolds Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@e720b71 Item: Title: 2.2 Holmes-Thompson volume and area in normed spaces Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1b26f7b2 Item: Title: 2.3 Crofton formula for hypersurfaces in Minkowski spaces Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@491cc5c9 Item: Title: 2.4 Holmes-Thompson duality formula Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@74ad1f1f Item: Title: 3 Strict convexity and properness Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@6a1aab78 Children: Item: Title: 3.1 Proof of the strict convexity Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@462d5aee Item: Title: 3.2 Proof of the properness Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@69b0fd6f Item: Title: 3.3 A new affine-invariant point Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@757942a1 Item: Title: 3.4 Further study of the strict convexity Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4a87761d Item: Title: 4 Equiaffine differential geometry Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@66d1af89 Item: Title: 5 Measure of lines in terms of hyperplanes Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@8646db9 Children: Item: Title: 5.1 Technical lemmas Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@37374a5e Item: Title: 5.2 Proof of Proposition 5.2 Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4671e53b Item: Title: 6 First variation of the dual area under translations Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@2db7a79b Children: Item: Title: 6.1 Preliminaries Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@6950e31 Item: Title: 6.2 Proof of Theorem 1.4 Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@b7dd107 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@42eca56e Info: Title: The Santaló point for the Holmes-Thompson boundary area Author: Florent Balacheff Subject: Advances in Mathematics, 397 (2022) 108118. 10.1016/j.aim.2021.108118 Creator: Elsevier Producer: Acrobat Distiller 9.5.5 (Windows) 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FontName: HPLFAH+LMMathItalic7-Regular Flags: Symbolic, Italic FontBBox: -1, -250, 1171, 750 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true XMP: application/pdf doi:10.1016/j.aim.2021.108118 The Santaló point for the Holmes-Thompson boundary area Florent Balacheff Gil Solanes Kroum Tzanev Convex body Crofton formula Holmes-Thompson area and volume Minkowski geometry Santaló point Symplectic geometry Advances in Mathematics, 397 (2022) 108118. 10.1016/j.aim.2021.108118 Elsevier Inc. journal Advances in Mathematics © 2021 The Authors. 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