On Stable Capillary Hypersurfaces with Planar Boundaries
Résumé
We study stable immersed capillary hypersurfaces Σ in domains B of R n+1 bounded by hyperplanes. When B is a half-space, we show Σ is a spherical cap. When B is a domain bounded by k hyperplanes P 1 ,. .. , P k , 2 ≤ k ≤ n + 1, having independent normals, and Σ has contact angle θ i with P i and does not touch the edges of B, we prove there exists δ > 0, depending only on P 1 ,. .. , P k , so that if θ i ∈ (π 2 − δ, π 2 + δ) for each i, then Σ has to be a piece of a sphere.
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