{"paper":{"title":"Pseudo-spherical Surfaces of Low Differentiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ivan Sterling, Josef F. Dorfmeister","submitted_at":"2013-01-24T00:31:21Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5679","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}