Gerard P. Barbanson
Whitney Regularity of the Image of the Chevalley Mapping
(43K, AMS - LaTeX)

ABSTRACT.   A closed set $F$ is Whitney 1-regular if for each compact $K\subset F$, 
 the geodesic distance in $K$ is equivalent to the Euclidean distance. 
 Let $P$ be the Chevalley map defined by an integrity basis of 
 the algebra of polynomials invariant by a reflection group, this note 
 gives the Whitney regularity of the image $P({\mathbb R}^n)$. 
 The proof uses ideas in [1], [3], [7] and [8] and needs a generalization 
 to the Jacobian of the Chevalley mappings of a property of Van der Monde determinants.