Existence of hypersurfaces with prescribed mean curvature I โ generic min-max
Existence of hypersurfaces with prescribed mean curvature I โ generic min-max
We prove that, for a generic set of smooth prescription functions $h$ on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean curvature $h$. The solution is either an embedded minimal hypersurface with integer multiplicity, or a non-minimal almost embedded hypersurface of multiplicity one. โฆ