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arXiv · 2509.24154

Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$

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

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Elham Matinpour. 2025-09-29. Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$. https://arxiv.org/abs/2509.24154

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