2010/11/30 by Cosimo Senni, Senni, Cosimo · 1 citation
Computer Science · Mathematics · #35J93 53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J93 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1011.6583
openalex publication_date 2010/11/30 · arxiv created 2011/03/28 · arxiv updated 2011/03/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold ℍ2 × \R, where ℍ2 is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature h ∈ (0, 1/2] on circular annuli of ℍ2. For 0 < h < 1/2 we obtain an estimate from above on any circular annulus and one from below on annuli with a small hole, the size of the hole depending on h. For h = 1/2 we obtain both estimates for any circular annulus. All the estimates depend only on the thickness of the annulus and the value of the graph on the outer boundary.