On the existence of geodesic connecting Lagrangian graphs in $\mathbb{C}^n$

Yiyan Xu

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arXiv · 1512.08423

On the existence of geodesic connecting Lagrangian graphs in $\mathbb{C}^n$

Yiyan Xu

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Abstract

In this paper we show that two Lagrangian graphs over the torus in $\mathbb{C}^n$ with large Lagrangian phase can be connected via Lipschitz continuous geodesic with respect to the $L^2$ metric on the space of Lagrangian submanifolds. In particular, the geodesic for Lagrangian graphs over the torus in $\mathbb{C}^n$ can be formulated as a degenerate elliptic equation, and we construct geodesic by solving the corresponding Dirichlet problem.

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Yiyan Xu. 2015-12-28. On the existence of geodesic connecting Lagrangian graphs in $\mathbb{C}^n$. https://arxiv.org/abs/1512.08423

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