2025/10/23 by Frauenfelder, Urs, Weber, Joa
#57R58 47A53 46B70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2510.20945
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 almost extendable weak Hessian~field. Our main result is a Fredholm theorem for Robbin-Salamon operators associated to non-continuous Hessians which we prove by taking advantage of this new structure.