English

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 C2\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.

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}
}