New affine inequalities and projection mean ellipsoids

New affine inequalities and projection mean ellipsoids

A variational formula for the Lutwak affine surface areas Λ j of convex bodies in R n is established when 1 ≤ j ≤ n - 1 . By using introduced new ellipsoids associated with projection functions of convex bodies, we prove a sharp isoperimetric inequality for Λ j , which opens up a new passage to atta...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Calculus of variations and partial differential equations 2019-04, Vol.58 (2), p.1-18, Article 44
Hauptverfasser: Zou, Du, Xiong, Ge
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Ellipsoids
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A variational formula for the Lutwak affine surface areas Λ j of convex bodies in R n is established when 1 ≤ j ≤ n - 1 . By using introduced new ellipsoids associated with projection functions of convex bodies, we prove a sharp isoperimetric inequality for Λ j , which opens up a new passage to attack the longstanding Lutwak conjecture in convex geometry.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-019-1497-0