A minimum principle for Lagrangian graphs
Symplectic Geometry
2023-09-19 v1 Analysis of PDEs
Abstract
The classical minimum principle is foundational in convex and complex analysis and plays an important role in the study of the real and complex Monge-Ampere equations. This note establishes a minimum principle in Lagrangian geometry. This principle relates the classical Lagrangian angle of Harvey-Lawson and the space-time Lagrangian angle introduced recently by Rubinstein-Solomon. As an application, this gives a new formula for solutions of the degenerate special Lagrangian equation in space-time in terms of the (time) partial Legendre transform of a family of solutions of obstacle problems for the (space) non-degenerate special Lagrangian equation.
Keywords
Cite
@article{arxiv.1606.08818,
title = {A minimum principle for Lagrangian graphs},
author = {Tamás Darvas and Yanir A. Rubinstein},
journal= {arXiv preprint arXiv:1606.08818},
year = {2023}
}