Multiplicity one and strictly stable Allen-Cahn minimal hypersurfaces

Published 19 Dec 2019 in math.DG and math.AP | (1912.08997v2)

Abstract: We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegenerate hypersurfaces with multiplicity one. Our results work in all dimensions and without variational assumptions on the Allen-Cahn solutions.

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