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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2104.03689 |
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Table of Contents:
- We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in $d=2$ to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in $d\geq 2$.