Busemann's intersection inequality in hyperbolic and spherical spaces
| Autor: | Jaegil Kim, Vladyslav Yaskin, Susanna Dann |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Inequality General Mathematics media_common.quotation_subject 010102 general mathematics Regular polygon Metric Geometry (math.MG) 01 natural sciences Measure (mathematics) Ellipsoid Intersection Mathematics - Metric Geometry 0103 physical sciences FOS: Mathematics Primary: 52A55 52A20 52A38 52A40 010307 mathematical physics 0101 mathematics media_common Mathematics |
| DOI: | 10.48550/arxiv.1706.06776 |
| Popis: | Busemann's intersection inequality asserts that the only maximizers of the integral $\int_{S^{n-1}} |K\cap\xi^\perp|^n d\xi$ among all convex bodies of a fixed volume in $\mathbb R^n$ are centered ellipsoids. We study this question in the hyperbolic and spherical spaces, as well as general measure spaces. Comment: 35 pages, 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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