The Morse-Sard-Brown Theorem for Functionals on Bounded-Fréchet-Finsler Manifolds

Abstract

In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded-Fréchet-Finsler manifold endowed with a strengthened connection $\mathcal{K}$ and if $\xi$ is a smooth Lipschitz-Fredholm vector field on $M$ with respect to $\mathcal{K}$ which satisfies condition (CV). Then, for any smooth functional $l$ on $M$ which is associated to $\xi$, the set of the critical values of $l$ is of the first category in $\rr$. Therefore, the set of the regular values of $l$ is a residual Baire subset of $\mathbb{R}$.

arXiv commentIn this version, some corrections were made to the printed version. arXiv admin note: text overlap with arXiv:1004.4900, arXiv:1303.1128