Geodesics of positive Lagrangians from special Lagrangians with boundary

Jake P. Solomon; Amitai M. Yuval

Corpus ID: 219573813

Geodesics of positive Lagrangians from special Lagrangians with boundary

@article{Solomon2020GeodesicsOP,
  title={Geodesics of positive Lagrangians from special Lagrangians with boundary},
  author={Jake P. Solomon and Amitai M. Yuval},
  journal={arXiv: Symplectic Geometry},
  year={2020}
}

Jake P. Solomon, Amitai M. Yuval

Published 2020

Mathematics

arXiv: Symplectic Geometry

Geodesics in the space of positive Lagrangian submanifolds are solutions of a fully non-linear degenerate elliptic PDE. We show that a geodesic segment in the space of positive Lagrangians corresponds to a one parameter family of special Lagrangian cylinders, called the cylindrical transform. The boundaries of the cylinders are contained in the positive Lagrangians at the ends of the geodesic. The special Lagrangian equation with positive Lagrangian boundary conditions is elliptic and the… CONTINUE READING

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