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Pré-Publication, Document De Travail 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 vertices 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-03410986 , version 1 (01-11-2021)
hal-03410986 , version 2 (14-11-2021)
hal-03410986 , version 3 (07-01-2022)

Identifiants

Citer

Rabah Souam. On stable capillary hypersurfaces with planar boundaries. 2022. ⟨hal-03410986v3⟩
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