2009/11/19 by José M. Espinar, Jose M. Espinar, Espinar, Jose M.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG
paper · pdf · doi:10.48550/arxiv.0911.3767
Section 4 has changed completely
openalex publication_date 2009/11/19 · arxiv created 2011/05/17 · arxiv updated 2011/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider differential operators L acting on functions on a Riemannian surface, Σ, of the form L = Δ+ V -a K ,where Δ is the Laplacian of Σ, K is the Gaussian curvature, a is a positive constant and V ∈ C∞(Σ). Such operators L arise as the stability operator of Σ immersed in a Riemannian three-manifold with constant mean curvature (for particular choices of V and a). We assume L is nonpositive acting on functions compactly supported on Σ. If the potential, V:= c + P with c a nonnegative constant, verifies either an integrability condition, i.e. P ∈ L1(Σ) and P is non positive, or a decay condition with respect to a point p0 ∈ Σ, i.e. |P(q)|≤ M/d(p0,q) (where d is the distance function in Σ), we control the topology and conformal type of Σ. Moreover, we establish a \it Distance Lemma. We apply such results to complete oriented stable H-surfaces immersed in a Killing submersion.