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
Received: 2014-1-9
Revised: 2014-5-8
Published Online: 2016-1-16
Published in Print: 2016-1-1
© 2016 by Walter de Gruyter Berlin/Boston
