Isometric disks are holomorphic
Complex Variables
2015-10-27 v1 Differential Geometry
Geometric Topology
Abstract
This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichm\"uller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichm\"uller disk. Additionally, a similar result is proved for a large class of disk-rigid domains, which includes strictly convex bounded domains, as well as Teichm\"uller spaces.
Keywords
Cite
@article{arxiv.1510.07335,
title = {Isometric disks are holomorphic},
author = {Stergios M. Antonakoudis},
journal= {arXiv preprint arXiv:1510.07335},
year = {2015}
}
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9 pages