The study of maximal surfaces by Lie symmetry

Mohammadpouri, Akram; Hasannejad, Sedigheh; Haji Badali, Ali

doi:10.22034/cmde.2024.62234.2729

The study of maximal surfaces by Lie symmetry

Document Type : Research Paper

Authors

¹ Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran.

² Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.

10.22034/cmde.2024.62234.2729

Abstract

Maximal surfaces, a fascinating class of surfaces in differential geometry, are identified by having a mean curvature equal to zero. This distinctive feature gives rise to a nonlinear second-order partial differential equation. In this current article, we delve into the symmetries that underlie the maximal surface equation. Next, we identify a one-dimensional optimal system of subalgebras that span these symmetries. It provides a powerful tool to analyze and manipulate the equation, making it easier to study. Finally, since we aim not only to explore the underlying symmetries of the maximal surface equation, we demonstrate how these symmetries can be harnessed to uncover and classify a wide range of maximal surfaces by using reduction methods.

Keywords

Main Subjects

Numerical methods for partial differential equations, boundary value problems

References

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