2008/08/21 by José M. Espinar, Jose M. Espinar, Espinar, Jose M. +2
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.DG
paper · pdf · doi:10.48550/arxiv.0808.3011
openalex publication_date 2008/08/21 · arxiv created 2009/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider operators L acting on functions on a Riemannian surface, Σ, of the form L = Δ+ V +a K. Here Δ is the Laplacian of Σ, V a non-negative potential on Σ, K the Gaussian curvature and a is a non-negative constant. Such operators L arise as the stability operator of Σ immersed in a Riemannian 3-manifold with constant mean curvature (for particular choices of V and a). We assume L is nonpositive acting on functions compactly supported on Σ and we obtain results in the spirit of some theorems of Ficher-Colbrie-Schoen, Colding-Minicozzi, and Castillon. We extend these theorems to a ≤ 1/4. We obtain results on the conformal type of Σ and a distance (to the boundary) lemma.