Uniqueness results for the Minkowski problem extended to hedgehogs

• Autorzy: Yves Martinez-Maure
• Języki publikacji: EN

Abstrakty

EN

The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere $\mathbb{S}^n $ of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.

Słowa kluczowe

EN

Minkowski problem; Monge-Ampère equations; Convex surfaces; Hedgehogs

Kategorie tematyczne

• 35M10: Equations of mixed type
• 53C45: Global surface theory (convex surfaces \`a la A. D. Aleksandrov)
• 53A05: Surfaces in Euclidean space
• 35A02: Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 440-450

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Yves Martinez-Maure

• Universités Paris 4 et Paris 7

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0134-8