• Corpus ID: 204743793

Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space

  title={Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space},
  author={Feng Luo and Tianqi Wu},
  journal={arXiv: Geometric Topology},
  • F. Luo, Tianqi Wu
  • Published 17 October 2019
  • Mathematics
  • arXiv: Geometric Topology
We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain. It provides a new way to approach the Koebe's conjecture using convex geometry. Combining our result with the work of He-Schramm on the Koebe conjecture, one establishes that every simply connected non-compact polyhedral surface is discrete conformal to the… 

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