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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.
Forward citations
Cited by 2 Pith papers
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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.
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Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds
Closed embedded CMC surfaces with |H|≥1 in finite-volume hyperbolic 3-manifolds have area bounded in terms of H and genus, and Bryant surfaces have area bounded linearly by genus.
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