On the Shape Fields Finiteness Principle

Abstract

In this paper, we improve the finiteness constant for the finiteness principles for $C^m({\mathbb{R}}^n,{\mathbb{R}}^d)$ and $C^{m-1,1}({\mathbb{R}}^n,{\mathbb{R}}^D)$ selection proven by Fefferman, Israel, and the second author and extend the more general shape fields finiteness principle to the vector-valued case.

17 pages