Minding's Theorem for Low Degrees of Differentiability

TL;DR

This paper extends Minding's Theorem to certain classes of low differentiability immersions, specifically $C^2$ and $C^{1M}$, with constant negative Gauss curvature, broadening its applicability.

Contribution

It proves Minding's Theorem for $C^2$-immersions and $C^{1M}$-immersions, which are less smooth than traditionally considered, thus expanding the theorem's scope.

Findings

Minding's Theorem holds for $C^2$-immersions with constant negative Gauss curvature.

The theorem is also valid for $C^{1M}$-immersions as defined in prior work.

This broadens the class of surfaces for which Minding's Theorem applies.

Abstract

We prove Minding's Theorem for $C^2$-immersions with constant negative Gauss curvature. As a Corollary we also prove Minding's Theorem for $C^{1M}$-immersions in the sense of \cite{DS}.