The Björling problem for prescribed mean curvature surfaces in ℝ³

2018/05/06 by Bueno, Antonio
#53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.02251

Abstract

In this paper we solve the Björling problem for the class of immersed surfaces in ℝ³ whose mean curvature is given as an analytic function depending on its Gauss map. As an application, we prove the existence of surfaces with the topology of a Möbius strip for an arbitrary large class of prescribed functions. In particular, we use the Björling problem to construct the first known examples of self-translating solitons of the mean curvature flow with the topology of a Möbius strip in ℝ³

Related

• The global geometry of surfaces with prescribed mean curvature in\n \ℝ³
• Surfaces of prescribed linear Weingarten curvature in ℝ³
• Notes on translating solitons for Mean Curvature Flow
• Ruled surfaces of generalized self-similar solutions of the mean\n curvature flow
• Complete translating solitons to the mean curvature flow in ℝ³ with nonnegative mean curvature