Equilibrium of Surfaces in a Vertical Force Field

In this paper, we study φ -minimal surfaces in R 3 when the function φ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in R 2 . We describe a full classification of complete flat-embedded φ -minimal surfaces if φ is strictly monoto...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 3
Main Authors: Martínez, Antonio, Martínez-Triviño, A. L.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Minimal surfaces
Translations
Vertical forces
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Summary:In this paper, we study φ -minimal surfaces in R 3 when the function φ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in R 2 . We describe a full classification of complete flat-embedded φ -minimal surfaces if φ is strictly monotone and characterize rotational φ -minimal surfaces by its behavior at infinity when φ has a quadratic growth.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01877-4