Generalized Legendre Transform of Conformally Flat Metrics

• Published in: Journal 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
• Language: English
• 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

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...