De nouvelles inégalités géométriques pour les hérissons

Advances in Applied Mathematics

2018

Self Cite

In this paper, we will try to argue and to show through fundamental examples that (a very huge class of) marginally trapped surfaces arise naturally from a 'lightlike co-contact structure', exactly in the same way as Legendrian fronts arise from a contact one (by projection of a Legendrian submanifold to the base of a Legendrian …bration), and that there is an adjunction relationship between both notions. We especially focus our interest on marginally trapped hedgehogs and study their relationships with Laguerre geometry and Brunn-Minkowski theory.

“…[7]), and then In the same vein as Theorem 5, we can notice that the signed surface area of the mean evolute H @ 2 h of H h is given by:…”

Section: Classical Isoperimetric Inequalities Involving Evolutes For mentioning

confidence: 74%

New insights on marginally trapped surfaces: The hedgehog theory point of view

Advances in Applied Mathematics

2018

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“…We shall see that any real function of class C 2 on S n is the support function of some hedgehog in R n+1 . In [8], the author gave the following partial extension of the Alexandrov-Fenchel inequality to hedgehogs under the assumption that l 3 , . .…”

Section: Partial Extensions To Hedgehogsmentioning

confidence: 99%

A stability estimate for the Aleksandrov–Fenchel inequality under regularity assumptions

2016

Monatsh Math

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“…where R (h2;:::; hn+1) denotes the mixed curvature function of H h2 ; : : : ; H hn+1 [10]: See [7] for a study of this extension of the mixed volume and Alexandrov-Fenchel type inequalities for hedgehogs.…”

Section: Hedgehog Theorymentioning

confidence: 99%

Hedgehog theory via Euler calculus

2014

Beitr Algebra Geom

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Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski di¤erences of convex bodies in 4 n+1 . They are the natural geometrical objects when one seeks to extend parts of the Brunn-Minkowski theory to a vector space which contains convex bodies. There is a close relationship between Minkowski addition and convolution with respect to the Euler characteristic. In this paper, we extend it to hedgehogs with an analytic support function. In this context, resorting only to the support functions and the Euler characteristic, we give various expressions for the index of a point with respect to a hedgehog. Finally, we present some applications.