Generalized Legendre Transform of Conformally Flat Metrics

In the calculus of variations, an important role is played by the Minkowski duality, or the Legendre transform of convex functions. We consider weakly regular, conformally flat Riemannian metrics of nonnegative curvature defined on the n -dimensional unit sphere. For this class of metrics, an analog...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 277; no. 5; pp. 760 - 769
Main Authors Kurkina, M. V., Rodionov, E. D., Semenov, S. P., Slavsky, V. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2023
Springer Nature B.V
Subjects
Calculus of variations
Mathematical analysis
Mathematics
Mathematics and Statistics
53A07
Lobachevsky space
Legendre transform
conformally flat metric
Online AccessGet full text

Cover

More Information
Summary:In the calculus of variations, an important role is played by the Minkowski duality, or the Legendre transform of convex functions. We consider weakly regular, conformally flat Riemannian metrics of nonnegative curvature defined on the n -dimensional unit sphere. For this class of metrics, an analog of the Legendre transformation is introduced and studied in detail.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06884-2