A note on the Morse index of 2k-ended phase transitions in R²

2017/05/22 by Christos Mantoulidis, Mantoulidis, Christos
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1705.07580

openalex publication_date 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R² is >= k-1. This bound is expected to be sharp.

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