Work

Relaxation of the area of the vortex map: A non-parametric Plateau problem for a catenoid containing a segment

Year: 2025

Type: article

Abstract: Motivated by the study of the non-parametric area $\mathcal A$ of the graph of the vortex map $u$ (a two-codimensional singular surface in $\mathbb R^4$) over the disc $Ω\subset \mathbb R^2$ of radius $l$, we perform a careful analysis of the singular part of the relaxation of $\mathcal A$ computed at $u$. The precise description is given in terms of a area-minimizing surface in a vertical copy of $\mathbb R^3 \subset \mathbb R^4$, which is a sort of ``catenoid'' containing a segment corresponding to a radius of $Ω$. The problem involves an area-minimization with a free boundary part; several boundary regularity properties of the minimizer are inspected.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110947

Authors: Giovanni Bellettini, Alaa Elshorbagy, Riccardo Scala

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250