Work

Stability of vertical minimal surfaces in three-dimensional sub-Riemannian manifolds

Year: 2025

Type: article

Abstract: We obtain first and second variation formulae for minimal surfaces in three-dimensional sub-Riemannian manifolds which are vertical, i.e., perpendicular to the horizontal distribution of the sub-Riemannian structure. We use these formulae to explore the connection between Riemannian and sub-Riemannian properties of a surface. We also describe vertical minimal surfaces of left-invariant sub-Riemannian structures on some three-dimensional Lie groups and find out whether they are stable.

Source: Proceedings of the International Geometry Center

DOI: 10.15673/pigc.v18i2.3009

Authors: Eugene Petrov, Ihor Havrylenko

Institution: V. N. Karazin Kharkiv National University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7083452024

FWCI: 1.876

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Cited by: 1

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