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On Complex Legendre Duality

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Abstract

Complex Legendre duality is a generalization of Legendre transformation from Euclidean spaces to Kähler manifolds that Berndtsson, Cordero-Erausquin, Klartag, and Rubinstein have recently constructed. It is a local isometry of the space of Kähler potentials. We show that the fixed point of such a transformation must correspond to a real analytic Kähler metric.

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Acknowledgements

This research was done while I enjoyed the hospitality of the Center for Advanced Study of the Norwegian Academy of Sciences. In addition, it was partially supported by NSF Grant DMS-1464150.

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  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA

    László Lempert

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  1. László Lempert
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Correspondence to László Lempert.

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Lempert, L. On Complex Legendre Duality. J Geom Anal 30, 2581–2592 (2020). https://doi.org/10.1007/s12220-017-9914-0

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