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...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-12, Vol.277 (5), p.760-769
Hauptverfasser: Kurkina, M. V., Rodionov, E. D., Semenov, S. P., Slavsky, V. V.
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Rodionov, E. D.
Semenov, S. P.
Slavsky, V. V.
description 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.
doi_str_mv 10.1007/s10958-023-06884-2
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subjects Calculus of variations
Mathematical analysis
Mathematics
Mathematics and Statistics
title Generalized Legendre Transform of Conformally Flat Metrics
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