MORSE THEORY WITH LOW DIFFERENTIABILITY AND DEGENERATE CRITICAL POINTS FOR FUNCTIONAL ENERGY OF A FINSLER METRIC

Abstract

The aim of this paper is to extend the Morse theory of $(\mathrm{\Lambda }M,E)$ with low differentiability and degenerate critical points, where $\mathrm{\Lambda }M$ is the space of $H^1$-closed curves on an $n$-dimensional compact manifold $M$ endowed with a Finsler metric $F:TM\to R$ and $F:\mathrm{\Lambda }M\to R$ is the associated energy integral, or simply the energy.