LIFTING DIFFERENTIABLE CURVES FROM ORBIT SPACES |
| |
Authors: | ADAM?PARUSI?SKI Email author" target="_blank">ARMIN?RAINEREmail author |
| |
Institution: | 1.Université Nice Sophia Antipolis,CNRS, LJAD UMR 7351,Nice,France;2.Fakult?t für Mathematik,Universit?t Wien,Wien,Austria |
| |
Abstract: | Let ρ: G → O(V) be a real finite dimensional orthogonal representation of a compact Lie group, let σ = (σ 1, ?, σn): V → ? n , where σ 1, ?, σn n form a minimal system of homogeneous generators of the G-invariant polynomials on V, and set d = maxi deg σ i . We prove that for each C d?1,1-curve c in σ(V) ?? n there exits a locally Lipschitz lift over σ, i.e., a locally Lipschitz curve \( \overline{c} \) in V so that c = σ ° \( \overline{c} \), 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 σ(V) admits a C 1-lift. For finite groups G we deduce a multivariable version and some further results. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|