Finite Area and Volume of Pointed k-Surfaces

Graham Smith
(Please use for correspondence this email).

Submission date: 03. Sep. 2007
Pages: 20
MSC-Numbers: 53C42, 30F60, 51M10, 53C45, 58D10
Keywords and phrases: immersed hypersurfaces, plateau problem, Gaussian curvature, hyperbolic space, moduli spaces, Teichmueller theory
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Abstract:
We define the ``volume'' contained by pointed k-surfaces, first studied by the author in [9], and we show that this volume is always finite. Likewise, we show that the surface area of a pointed k-surface is always finite.