https://neckpinch.com/authors/a-l-martinez-trivino/New arXiv papers by A. L. Martínez-Triviño, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2107.13918/arxiv:2107.13918Thu, 29 Jul 2021 00:00:00 GMTA. L. Martínez-Triviño, J. P. dos Santos — 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.Mean curvature flowSelf-shrinkers & translatorsStability & uniqueness