Communications in Analysis and Geometry
Volume 27 (2019)
A minimum principle for Lagrangian graphs
Pages: 857 – 876
The classical minimum principle is foundational in convex and complex analysis and plays an important rôle in the study of the real and complex Monge–Ampère 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.
Received 29 June 2016
Accepted 7 April 2017
Published 8 October 2019