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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 198, Issue 4, pp 1471–1479 | Cite as

Surfaces with a canonical principal direction and prescribed mean curvature

  • Rafael López
  • Gabriel Ruiz-HernándezEmail author
Article
  • 136 Downloads

Abstract

A surface in Euclidean space has a canonical principal direction with respect to a fixed direction \({{\mathbf {d}}}\) if its tangent part \({{\mathbf {d}}}^\top \) is a principal direction along the surface. In this paper, we classify all such surfaces with prescribed mean curvature given as an affine function of one of the following three functions: the height function, the angle function and the support function.

Keywords

Principal direction Mean curvature Capillary surface Self-shrinker Translating soliton 

Mathematics Subject Classification

53B25 

Notes

Acknowledgements

The second author wants to thanks the Departamento de Geometría y Topología and the Instituto de Matemáticas (IEMath-GR) of Universidad de Granada for the hospitality, facilities and inspiring ambient during this sabbatical year. He is also grateful with his institution UNAM by this opportunity of a sabbatical period supported by the program PASPA of DGAPA.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR)Universidad de GranadaGranadaSpain
  2. 2.Instituto de Matemáticas, Unidad JuriquillaUniversidad Nacional Autónoma de MéxicoQuerétaroMéxico

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