Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$
Differential Geometry
2025-09-30 v1
Abstract
We investigate the geometric constraints imposed by low Morse index on minimal surfaces with Y-singularities, focusing on the classification of those with Morse index one. Our rigidity result establishes a partial uniqueness theorem, highlighting the Y-catenoid as a distinguished example among complete, two-sided minimal surfaces in with Y-singularities and Morse index one.
Cite
@article{arxiv.2509.24154,
title = {Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$},
author = {Elham Matinpour},
journal= {arXiv preprint arXiv:2509.24154},
year = {2025}
}