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arXiv · 1301.5679

Pseudo-spherical Surfaces of Low Differentiability

Josef F. Dorfmeister·Ivan Sterling
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Abstract

We continue our investigations into Toda's algorithm [14,3]; a Weierstrass-type representation of Gauss curvature $K=-1$ surfaces in $\mathbb{R}^3$. We show that $C^0$ input potentials correspond in an appealing way to a special new class of surfaces, with $K=-1$, which we call $C^{1M}$. These are surfaces which may not be $C^2$, 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 $C^{1M}$ version of Hilbert's Theorem.

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Josef F. Dorfmeister, Ivan Sterling. 2013-01-24. Pseudo-spherical Surfaces of Low Differentiability. https://arxiv.org/abs/1301.5679

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