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 inMediterranean journal of mathematics Vol. 19; no. 1
Main Authors Martínez, Antonio, Martínez-Triviño, A. L.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2022
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Minimal surfaces
Translations
Vertical forces
53C42
minimal
weighted volume functional
35J60
elliptic equation
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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