Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 182, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 4, 2020.
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Kurkina, M.V., Rodionov, E.D., Semenov, S.P. et al. Generalized Legendre Transform of Conformally Flat Metrics. J Math Sci 277, 760–769 (2023). https://doi.org/10.1007/s10958-023-06884-2
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DOI: https://doi.org/10.1007/s10958-023-06884-2