{"paper":{"title":"Lifting differentiable curves from orbit spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Adam Parusinski, Armin Rainer","submitted_at":"2014-06-10T09:49:10Z","abstract_excerpt":"Let $\\rho : G \\rightarrow \\operatorname{O}(V)$ be a real finite dimensional orthogonal representation of a compact Lie group, let $\\sigma = (\\sigma_1,\\ldots,\\sigma_n) : V \\to \\mathbb R^n$, where $\\sigma_1,\\ldots,\\sigma_n$ form a minimal system of homogeneous generators of the $G$-invariant polynomials on $V$, and set $d = \\max_i \\operatorname{deg} \\sigma_i$. We prove that for each $C^{d-1,1}$-curve $c$ in $\\sigma(V) \\subseteq \\mathbb R^n$ there exits a locally Lipschitz lift over $\\sigma$, i.e., a locally Lipschitz curve $\\overline c$ in $V$ so that $c = \\sigma \\circ \\overline c$, and we obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2485","kind":"arxiv","version":3},"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"}