Uniqueness in the Plateau problem near Quadratic cones
Differential Geometry
2025-09-22 v1
Abstract
We consider minimal hypersurfaces inside the unit ball whose boundary on the sphere is a small perturbation of the link of a minimizing quadratic cone. We show that such minimal surfaces are uniquely determined by their boundary condition. In particular the solutions of the Plateau problem are unique for boundary conditions given by small perturbations of the link of a quadratic cone.
Cite
@article{arxiv.2509.15503,
title = {Uniqueness in the Plateau problem near Quadratic cones},
author = {Vishnu Nandakumaran and Gábor Székelyhidi},
journal= {arXiv preprint arXiv:2509.15503},
year = {2025}
}
Comments
19 pages