Area estimates for capillary cmc hypersurfaces with nonpositive Yamabe invariant

2025/02/14 by Leandro F. Pessoa, Pessoa, Leandro F., Erisvaldo Véras +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.10171

openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove area estimates for stable capillary cmc (minimal) hypersurfaces Σ with nonpositive Yamabe invariant that are properly immersed in a Riemannian n-dimensional manifold M with scalar curvature R^M and mean curvature of the boundary H^{∂ M} bounded from below. We also prove a local rigidity result in the case Σ is embedded and J-energy-minimizing. In this case, we show that M locally splits along Σ and is isometric to (-ε,ε)× Σ, dt² + e^-2Htg), where g is Einstein, or Ricci flat, H≥ 0 and ∂Σ is totally geodesic.

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