Uniqueness of the [φ,e₃]-catenary cylinders by their asymptotic behaviour

2021/07/29 by A. L. Martínez-Triviño, Martínez-Triviño, A. L., João Paulo dos Santos +1
Engineering · #Differential Geometry (math.DG) #FOS: Mathematics #Mechanical Behavior of Composites #Railway Engineering and Dynamics #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2107.13918

openalex publication_date 2021/07/29 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We establish a uniqueness result for the [φ,e₃]-catenary cylinders by their asymptotic behaviour. Well known examples of such cylinders are the grim reaper translating solitons for the mean curvature flow. For such solitons, F. Martín, J. Pérez-García, A. Savas-Halilaj and K. Smoczyk proved that, if Σ is a properly embedded translating soliton with locally bounded genus, and C^∞-asymptotic to two vertical planes outside a cylinder, then Σ must coincide with some grim reaper translating soliton. In this paper, applying the moving plane method of Alexandrov together with a strong maximum principle for elliptic operators, we increase the family of [φ,e₃]-minimal graphs where these types of results hold under different assumption of asymptotic behaviour.

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