Minimal surfaces and the new main inequality

2022/12/31 by Vladimir Marković, Markovic, Vladimir, Nathaniel Sagman +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2301.00249

openalex publication_date 2022/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the new main inequality as a minimizing criterion for minimal maps to products of ℝ-trees, and the infinitesimal new main inequality as a stability criterion for minimal maps to ℝⁿ. Along the way, we develop a new perspective on destabilizing minimal surfaces in ℝⁿ, and as a consequence we reprove the instability of some classical minimal surfaces; for example, the Enneper surface.

Related

• Unstable minimal surfaces in ℝⁿ and in products of hyperbolic surfaces
• Another property of minimal surfaces in Euclidean space
• Lectures on Minimal Surfaces
• A lemma on the minimal surfaces
• The min--max construction of minimal surfaces