Half-space theorems for properly immersed surfaces in \ℝ³\n with prescribed mean curvature

2019/01/14 by Antonio Bueno, Bueno, Antonio
Engineering · Mathematics · #34A26 #53A10 #53C42 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1901.04343

openalex publication_date 2019/01/14 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

Motivated by the large ammount of results obtained for minimal and positive\nconstant mean curvature surfaces in several ambient spaces, the aim of this\npaper is to obtain half-space theorems for properly immersed surfaces in\n\ℝ³ whose mean curvature is given as a prescribed function of its\nGauss map. In order to achieve this purpose, we will study the behavior at\ninfinity of a 1-parameter family of properly embedded annuli that are analogous\nto the usual minimal catenoids.\n

Related

• Mean convex properly embedded [φ,e₃]-minimal surfaces in ℝ³
• Complete surfaces of constant anisotropic mean curvature
• Complete Surfaces with Ends of Non Positive Curvature
• The global geometry of surfaces with prescribed mean curvature in\n \ℝ³
• A general halfspace theorem for constant mean curvature surfaces