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The linearized Floer equation in a chart (2510.20945v1)
Published 23 Oct 2025 in math.SG, math.AP, and math.FA
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.
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