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arXiv · 2108.00555

Convergence and Riemannian bounds on Lagrangian submanifolds

Jean-Philippe Chassé
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Abstract

We consider collections of Lagrangian submanifolds of a given symplectic manifold which respect uniform bounds of curvature type coming from an auxiliary Riemannian metric. We prove that, for a large class of metrics on these collections, convergence to an embedded Lagrangian submanifold implies convergence to it in the Hausdorff metric. This class of metrics includes well-known metrics such as the Lagrangian Hofer metric, the spectral norm and the shadow metrics introduced by Biran, Cornea and Shelukhin arXiv:1806.06630. The proof relies on a version of the monotonicity lemma, applied on a carefully-chosen metric ball.

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Jean-Philippe Chassé. 2021-08-01. Convergence and Riemannian bounds on Lagrangian submanifolds. https://arxiv.org/abs/2108.00555

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