Low complexity solutions of the Allen-Cahn equation on three-spheres

2018/03/13 by Robert Haslhofer, Mohammad N. Ivaki, Haslhofer, Robert +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1803.04830

arxiv created 2018/03/13 · arxiv updated 2018/03/14

Abstract

In this short note, we prove that on the three-sphere with any bumpy metric there exist at least four solutions of the Allen-Cahn equation with spherical interface and index at most two. The proof combines several recent results from the literature.

Related

• Rigidity of low index solutions on S³ via a Frankel theorem for the Allen-Cahn equation
• Allen-Cahn equation and degenerate minimal hypersurface
• Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere
• Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space
• From bubbles to clusters: Multiple solutions to the Allen--Cahn system