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Isometric disks are holomorphic (1510.07335v1)
Published 26 Oct 2015 in math.CV, math.DG, and math.GT
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.
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