Comptes Rendus
no. 8
Geometry/Differential geometry
A centro-projective inequality
[Une inégalité centro-projective]

Présenté par : the Editorial Board

Constantin Vernicos1 ; Deane Yang2
1 IMAG, Université de Montpellier, case courrier 051, place Eugène-Bataillon, 34395 Montpellier cedex, France
2 Department of Mathematics, Tandon School of Engineering, New York University, Six Metrotech Center, Brooklyn NY 11201, USA
Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 681-685.

Nous présentons une nouvelle formule pour l'aire centro-projective d'un corps convexe. Cette aire a été préalablement définie par Berck–Bernig–Vernicos. Nous utilisons cette formule pour montrer qu'elle est majorée par l'aire centro-projective d'une ellipse, l'égalité caractérisant les ellipsoïdes.

We give a new integral formula for the centro-projective area of a convex body, which was first defined by Berck–Bernig–Vernicos. We then use the formula to prove that it is bounded from above by the centro-projective area of an ellipsoid and that equality occurs if and only if the convex set is an ellipsoid.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.07.005

Constantin Vernicos 1 ; Deane Yang 2

1 IMAG, Université de Montpellier, case courrier 051, place Eugène-Bataillon, 34395 Montpellier cedex, France
2 Department of Mathematics, Tandon School of Engineering, New York University, Six Metrotech Center, Brooklyn NY 11201, USA 
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Constantin Vernicos; Deane Yang. A centro-projective inequality. Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 681-685. doi : 10.1016/j.crma.2019.07.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.07.005/

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