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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
79/2007

Finite Area and Volume of Pointed k-Surfaces

Graham Smith

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.

Received:
Sep 3, 2007
Published:
Sep 3, 2007
MSC Codes:
53C42, 30F60, 51M10, 53C45, 58D10
Keywords:
immersed hypersurfaces, plateau problem, Gaussian curvature, hyperbolic space, moduli spaces, Teichmueller theory

Related publications

Preprint
2007 Repository Open Access
Graham Smith

Finite area and volume of pointed \(k\)-surfaces