On the characteristic function of a strictly convex domain and the Fubini-Pick invariant
type: Item
instance of: scholarly article
title: On the characteristic function of a strictly convex domain and the Fubini-Pick invariant
zbMATH Open document ID: 0654.53012
DOI: 10.1007/BF03323252
author: Takeshi Sasaki
published in: Results in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The author's characteristic function of a convex body D in Euclidean n- space was used before for the definition of a projectively invariant metric in D. Here he gives a representation of the characteristic function in terms of a solution of a certain Monge-Ampère equation in D and of the Fubini-Pick invariant of \(\partial D\). Two characterizations of ellipsoids are corollaries.
Mathematics Subject Classification ID: 53A20
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 4067763
zbMATH Keywords: Bergman kernel function
zbMATH Keywords: characteristic function
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: Fubini-Pick invariant
zbMATH Keywords: characterizations of ellipsoids
MaRDI profile type: Publication
cites work: Sur les variétés localement affines et localement projectives
cites work: On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
cites work: Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains
cites work: Parabolic invariant theory in complex analysis
cites work: Local theory of affine hypersurfaces
cites work: A note on characteristic functions and projectively invariant metrics on a bounded convex domain
full work available at URL: https://doi.org/10.1007/bf03323252
OpenAlex ID: W2084632390
description: scientific article; zbMATH DE number 4067763