On the area of minimal surfaces in a slab

2015/03/10 by Jaigyoung Choe, Choe, Jaigyoung, Benôıt Daniel +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1503.02771

openalex publication_date 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a non-planar orientable minimal surface S in a slab which is possibly with genus or with more than two boundary components. We show that there exists a catenoidal waist W in the slab whose flux has the same vertical component as S such that Area(S)>= Area(W), provided the intersections of S with horizontal planes have the same orientation.

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