Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifting differentiable curves from orbit spaces   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 obtain explicit bounds for the Lipschitz constant of
$\overline c$ in terms of $c$. Moreover, we show that each $C^d$-curve in
$\sigma(V)$ admits a $C^1$-lift. For finite groups $G$ we deduce a
multivariable version and some further results.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th