The Björling problem for prescribed mean curvature surfaces in $\mathbb{R}^3$

Antonio Bueno

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arXiv · 1805.02251

The Björling problem for prescribed mean curvature surfaces in $\mathbb{R}^3$

Antonio Bueno

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Abstract

In this paper we solve the Björling problem for the class of immersed surfaces in $\mathbb{R}^3$ 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 $\mathbb{R}^3$

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BibTeX RIS

Antonio Bueno. 2019-03-18. The Björling problem for prescribed mean curvature surfaces in $\mathbb{R}^3$. https://arxiv.org/abs/1805.02251

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