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math.DG2020★ 1 cited
Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen--Cahn
Costante Bellettini
In Guaraco's 2018 work a new proof was given of the existence of a closed minimal hypersurface in a compact Riemannian manifold with . This was achieved by emplo…
math.DG2020★ 6 cited
The inhomogeneous Allen--Cahn equation and the existence of prescribed-mean-curvature hypersurfaces
Costante Bellettini, Neshan Wickramasekera
We prove that for any given compact Riemannian manifold of dimension and any non-negative Lipschitz function on , there exists a quasi-embedded, boundaryles…