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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 16, Issue 1

Issues

Pseudospherical surfaces of low differentiability

Josef F. Dorfmeister / Ivan Sterling
  • Corresponding author
  • Mathematics and Computer Science Department, St Mary’s College of Maryland, St Mary’s City, MD 20686-3001, USA
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Published Online: 2016-01-16 | DOI: https://doi.org/10.1515/advgeom-2015-0039

Abstract

We continue our investigations into Toda’s algorithm [14; 3], which gives a Weierstrass-type representation of Gauss curvature K = −1 surfaces in R3. We show that C0 input potentials correspond in an appealing way to a special new class of surfaces, with K = −1, which we call C1M. These are surfaces which may not be C2, but whose mixed second partials are continuous and equal. We also extend several results of Hartman-Wintner [5] concerning special coordinate changes which increase differentiability of immersions of K = −1 surfaces. We prove a C1M version of Hilbert’s Theorem.

Keywords: Constant Gauss curvature surfaces; loop groups

About the article

Received: 2014-01-09

Revised: 2014-05-08

Published Online: 2016-01-16

Published in Print: 2016-01-01


Citation Information: Advances in Geometry, Volume 16, Issue 1, Pages 1–20, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0039.

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