Higher-Dimensional Catenoid, Liouville Equation, and Allen-Cahn Equation

Abstract

We build a family of entire solutions to the Allen-Cahn equation in RN+1 for N >= 3, whose level set approaches the higher-dimensional catenoid in a compact region and has two logarithmic ends governed by the solutions to the Liouville equation. Keywords. KeyWords Plus:MINIMAL-SURFACES

CONJECTURE

ENDS

REGULARITY

MULTIPLE

GIORGI

CONES

R-3