Extremal discs and Segre varieties for real-analytic hypersurfaces in $\mathbb{C}^2$
Complex Variables
2020-09-15 v1
Abstract
We show that if the Segre varieties of a strictly pseudoconvex hypersurface in 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.
Keywords
Cite
@article{arxiv.2009.06049,
title = {Extremal discs and Segre varieties for real-analytic hypersurfaces in $\mathbb{C}^2$},
author = {Florian Bertrand and Giuseppe Della Sala and Bernhard Lamel},
journal= {arXiv preprint arXiv:2009.06049},
year = {2020}
}