Minimal Lagrangian connections on compact surfaces

Thomas Mettler

doi:10.1016/j.aim.2019.106747

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arXiv · 1609.08033

Minimal Lagrangian connections on compact surfaces

Thomas Mettler

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Abstract

We introduce the notion of a minimal Lagrangian connection on the tangent bundle of a manifold and classify all such connections in the case where the manifold is a compact oriented surface of non-vanishing Euler characteristic. Combining our classification with results of Labourie and Loftin, we conclude that every properly convex projective surface arises from a unique minimal Lagrangian connection.

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Thomas Mettler. 2016-09-26. Minimal Lagrangian connections on compact surfaces. https://doi.org/10.1016/j.aim.2019.106747

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