Séminaires :
Séminaire d'Analyse Fonctionnelle
Equipe(s) :
af,
Responsables :
E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle :
salle 13 - couloir 15-16 - 4ème étage
Adresse :
Campus Pierre et Marie Curie
Description
Le Jeudi à 10h30 - IMJ-PRG - 4 place Jussieu - 75005 PARIS
Lien vers les archives des années antérieures à 2015
Orateur(s)
Artem Zvavitch - Kent,
Titre
Bezout Inequality for Mixed volumes
Date
05/07/2018
Horaire
10:30 à 17:40
Diffusion
Résume
In this talk we will discuss the following analog of Bezout inequality for mixed volumes: $
V(P_1,\dots,P_r,\Delta^
n-r
)V_n(\Delta)^
r-1
\leq \prod_
i=1
^r V(P_i,\Delta^
n-1
)\ \text
for
2\leq r\leq n.
$ We will briefly explain the connection of the above inequality to the original Bezout inequality and show that the inequality is true when $\Delta$ is an $n$-dimensional simplex and $P_1, \dots, P_r$ are convex bodies in $
\mathbb R
^n$. We will present a conjecture that if the above inequality is true for all convex bodies $P_1, \dots, P_r$, then $\Delta$ must be an $n$-dimensional simplex. We will show that the conjecture is true in many special cases. Finally, we connect the inequality to an inequality on the volume of orthogonal projections of convex bodies as well as present an isomorphic version of the inequality.
Salle
salle 13 - couloir 15-16 - 4ème étage
Adresse
Campus Pierre et Marie Curie
© IMJ-PRG
