Regular Lagrangians are smooth Lagrangians
Abstract
We prove that for any element in the γ-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its γ-support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the γ-support of an element in the completion is compact, then it is connected.
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