Uniqueness results for the Minkowski problem extended to hedgehogs

Yves Martinez-Maure

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 440-450
  • ISSN: 2391-5455

Abstract

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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 𝕊 n of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.

How to cite

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Yves Martinez-Maure. "Uniqueness results for the Minkowski problem extended to hedgehogs." Open Mathematics 10.2 (2012): 440-450. <http://eudml.org/doc/269570>.

@article{YvesMartinez2012,
abstract = {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.},
author = {Yves Martinez-Maure},
journal = {Open Mathematics},
keywords = {Minkowski problem; Monge-Ampère equations; Convex surfaces; Hedgehogs; convex surfaces; hedgehogs},
language = {eng},
number = {2},
pages = {440-450},
title = {Uniqueness results for the Minkowski problem extended to hedgehogs},
url = {http://eudml.org/doc/269570},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Yves Martinez-Maure
TI - Uniqueness results for the Minkowski problem extended to hedgehogs
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 440
EP - 450
AB - 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.
LA - eng
KW - Minkowski problem; Monge-Ampère equations; Convex surfaces; Hedgehogs; convex surfaces; hedgehogs
UR - http://eudml.org/doc/269570
ER -

References

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