A parabolic minimal surface in R3 intersects every nonflat properly embedded minimal surface of bounded curvature

2022/06/13 by Franc Forstnerič, Forstneric, Franc
Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2206.06045

openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the image of a nonconstant conformal harmonic map \mathbb C→ \mathbb R³, not necessarily proper and possibly with branch points, intersects every properly embedded nonflat minimal surface of bounded curvature in \mathbb R³. The same holds if \mathbb C is replaced by any open conformal surface without nonconstant bounded subharmonic functions.

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