Annals of Global Analysis and Geometry

, Volume 56, Issue 1, pp 87–96 | Cite as

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

  • Antonio BuenoEmail author


In this paper we prove existence and uniqueness of 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 \(\mathbb {R}^3\).


Björling problem Prescribed mean curvature surfaces Möbius strip 

Mathematics Subject Classification

53A10 53C42 



The author was partially supported by MICINN-FEDER Grant No. MTM2016-80313-P, Junta de Andalucía Grant No. FQM325 and FPI-MINECO Grant No. BES-2014-067663. The author wants to express his gratitude to his Ph.D. advisor Pablo Mira, for fruitful conversations about this topic.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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