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Our main result is the $\mathcal{C}^0$-rigidity of the area spectrum and theMaslov class of Lagrangian submanifolds. This relies on the existence ofpunctured pseudoholomorphic discs in cotangent bundles with boundary on thezero section, whose boundaries represent any integral homology class. Wediscuss further applications of these punctured discs in symplectic geometry.

$\mathcal{C}^0$-rigidity of Lagrangian submanifolds and punctured holomorphic discs in the cotangent bundle