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Article Dans Une Revue The Journal of Geometric Analysis Année : 2023

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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Dates et versions

hal-04087042 , version 1 (02-05-2023)

Identifiants

Citer

Rabah Souam. On Stable Capillary Hypersurfaces with Planar Boundaries. The Journal of Geometric Analysis, 2023, 33 (6), pp.196. ⟨10.1007/s12220-023-01257-2⟩. ⟨hal-04087042⟩
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