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.
Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
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abstract
We prove the optimal $C^{1,1}$ regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescribed mean curvature in the round 3-sphere for an open dense set of prescribing functions with $L^{\infty}$ norm at most 0.547.
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math.DG 1years
2025 1verdicts
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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.