English

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 R3\mathbb{R}^3 with Y-singularities and Morse index one.

Keywords

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}
}