Comptes Rendus
Geometry/Differential geometry
A centro-projective inequality
Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 681-685.

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.

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.

Published online:
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
     author = {Constantin Vernicos and Deane Yang},
     title = {A centro-projective inequality},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {681--685},
     publisher = {Elsevier},
     volume = {357},
     number = {8},
     year = {2019},
     doi = {10.1016/j.crma.2019.07.005},
     language = {en},
AU  - Constantin Vernicos
AU  - Deane Yang
TI  - A centro-projective inequality
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 681
EP  - 685
VL  - 357
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2019.07.005
LA  - en
ID  - CRMATH_2019__357_8_681_0
ER  - 
%0 Journal Article
%A Constantin Vernicos
%A Deane Yang
%T A centro-projective inequality
%J Comptes Rendus. Mathématique
%D 2019
%P 681-685
%V 357
%N 8
%I Elsevier
%R 10.1016/j.crma.2019.07.005
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%F CRMATH_2019__357_8_681_0
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.

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