The linearized Floer equation in a chart

Abstract: In this article we are considering the Hessian of the area functional in a non-Darboux chart. This does not seem to have been considered before and leads to an interesting new mathematical structure which we introduce in this article and refer to as \emph{almost extendable weak Hessian~field}. Our main result is a Fredholm theorem for Robbin-Salamon operators associated to \emph{non-continuous} Hessians which we prove by taking advantage of this new structure.