| Autor: |
Ohad Giladi, Carsten Schütt, Elisabeth M. Werner, H. Huang |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Journal of Functional Analysis. 279:108531 |
| ISSN: |
0022-1236 |
| DOI: |
10.1016/j.jfa.2020.108531 |
| Popis: |
Given a convex body K ⊆ R n and p ∈ R , we introduce and study the extremal inner and outer affine surface areas I S p ( K ) = sup K ′ ⊆ K ( as p ( K ′ ) ) and o s p ( K ) = inf K ′ ⊇ K ( as p ( K ′ ) ) , where as p ( K ′ ) denotes the L p -affine surface area of K ′ , and the supremum is taken over all convex subsets of K and the infimum over all convex compact subsets containing K. The convex body that realizes I S 1 ( K ) in dimension 2 was determined in [3] where it was also shown that this body is the limit shape of lattice polytopes in K. In higher dimensions no results are known about the extremal bodies. We use a thin shell estimate of [23] and the Lowner ellipsoid to give asymptotic estimates on the size of I S p ( K ) and o s p ( K ) . Surprisingly, it turns out that both quantities are proportional to a power of volume. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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