Total curvature of complete surfaces in hyperbolic space

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Abstract

We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behavior. The result is given in terms of the measure of geodesics intersecting the surface non-trivially, and of a conformal invariant of the curve at infinity. © 2010 Elsevier Inc.
Original languageEnglish
Pages (from-to)805-825
JournalAdvances in Mathematics
Volume225
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • 53C65
  • Hyperbolic space
  • Integral geometry
  • Open surfaces
  • Total curvature

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