Calibrations associated to Monge-Ampere equations

2007/02/10 by Micah Warren, Warren, Micah · 1 citation
Mathematics · Physics and Astronomy · #35J60 #53C38 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:35J60 #msc:53C38

paper · pdf · doi:10.48550/arxiv.math/0702291

18 pages. typos corrected

openalex publication_date 2007/02/10 · arxiv created 2007/09/15 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the volume maximizing property of the special Lagrangian submanifolds of a pseudo-Euclidean space. These special Lagrangian submanifolds arise locally as gradient graphs of solutions to Monge-Ampere Equations.

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• Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow in \mathbb Rⁿ⁺¹_-

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