In this paper we discuss nondegeneracy and stability properties of some special minimal hypersurfaces which are asymptotic to a given Lawson cone Cm,n, for m,n≥2. Then we use such hypersurfaces to construct solutions to the Allen-Cahn equation -Δu=u-u3 in RN+1, N+1≥8, whose zero level set has exactly k≥2 connected components and with infinite Morse index.
Lawson Cones and the Allen-Cahn Equation
Rizzi M.
2026-01-01
Abstract
In this paper we discuss nondegeneracy and stability properties of some special minimal hypersurfaces which are asymptotic to a given Lawson cone Cm,n, for m,n≥2. Then we use such hypersurfaces to construct solutions to the Allen-Cahn equation -Δu=u-u3 in RN+1, N+1≥8, whose zero level set has exactly k≥2 connected components and with infinite Morse index.File in questo prodotto:
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