A Liouville type theorem for special Lagrangian Equations with constraints

2007/06/05 by Micah Warren, Yu Yuan, Warren, Micah +1 · 6 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geotechnical and Geomechanical Engineering #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0706.0699

11 pages. Version to appear in CPDE

openalex publication_date 2007/06/05 · arxiv created 2008/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.

Cited by

• Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints
• Semi-convex viscosity solutions of the special Lagrangian equation
• Calibrated submanifolds with flat normal bundles
• Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow in \mathbb Rⁿ⁺¹_-
• Explicit gradient estimates for minimal Lagrangian surfaces of dimension two
• A quantitative stability result for regularity of optimal transport on compact manifolds

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