Minimal discs in hyperbolic space bounded by a quasicircle at infinity

  title={Minimal discs in hyperbolic space bounded by a quasicircle at infinity},
  author={Andrea Seppi},
  journal={arXiv: Differential Geometry},
  • Andrea Seppi
  • Published 13 November 2014
  • Mathematics
  • arXiv: Differential Geometry
We prove that the supremum of principal curvatures of a minimal embedded disc in hyperbolic three-space spanning a quasicircle in the boundary at infinity is estimated in a sublinear way by the norm of the quasicircle in the sense of universal Teichmuller space, if the quasicircle is sufficiently close to being the boundary of a totally geodesic plane. As a by-product we prove that there is a universal constant C independent of the genus such that if the Teichmuller distance between the ends of… 
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