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Existence of minimal hypersurfaces with non-empty free boundary for generic metrics
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Existence of minimal hypersurfaces with non-empty free boundary for generic metrics
classification
math.DG
math.APmath.GT
keywords
boundarycompactfreemetricsminimalpartialalmostbaire
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For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a compact manifold with boundary $(M^{n+1},\partial M)$, $3\leq (n + 1)\leq 7$, we prove that, for any open subset $V$ of $\partial M$, there exists a compact, properly embedded free boundary minimal hypersurface intersecting $V$.
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