On any closed 3-7 dimensional manifold that contains a strictly stable minimal surface, a large class of prescribed-mean-curvature functions admit infinitely many distinct almost embedded hypersurfaces.
Buchstaber and Taras E
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Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface
On any closed 3-7 dimensional manifold that contains a strictly stable minimal surface, a large class of prescribed-mean-curvature functions admit infinitely many distinct almost embedded hypersurfaces.