Extremal discs and Segre varieties for real-analytic hypersurfaces in $\mathbb{C}^2$

Florian Bertrand; Giuseppe Della Sala; Bernhard Lamel

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arXiv · 2009.06049

Extremal discs and Segre varieties for real-analytic hypersurfaces in $\mathbb{C}^2$

Florian Bertrand·Giuseppe Della Sala·Bernhard Lamel

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Abstract

We show that if the Segre varieties of a strictly pseudoconvex hypersurface in $\mathbb{C}^2$ are extremal discs for the Kobayashi metric, then that hypersurface has to be locally spherical. In particular, this gives yet another characterization of the unit sphere in terms of two important invariant families of objects coinciding.

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Florian Bertrand, Giuseppe Della Sala, Bernhard Lamel. 2020-09-13. Extremal discs and Segre varieties for real-analytic hypersurfaces in $\mathbb{C}^2$. https://arxiv.org/abs/2009.06049

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