Height estimates for H-surfaces in the warped product \mathbbM×_fℝ

2018/03/21 by Folha, Abigail, Peñafiel, Carlos, Santos, Walcy
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C42 #Secondary 53C30

paper · doi:10.48550/arxiv.1803.08107

Abstract

In this article, we consider compact surfaces Σ having constant mean curvature H (H-surfaces) whose boundary Γ=∂Σ⊂ \mathbbM₀= \mathbbM ×_f\0\ is transversal to the slice \mathbbM₀ of the warped product \mathbbM×_fℝ , here \mathbbM denotes a Hadamard surface. We obtain height estimate for a such surface Σ having positive constant mean curvature involving the area of a part of Σ above of \mathbbM ₀ and the volume it bounds. Also we give general conditions for the existence of rotationally-invariant topological spheres having positive constant mean curvature H in the warped product ℍ×_fℝ, where ℍ denotes the hyperbolic disc. Finally we present a non-trivial example of such spheres.

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