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A note on radial graphs with constant mean curvature
Authors:Rafael López
Institution:(1) Departamento de Geometría y Topología. Universidad de Granada. 18071 Granada, Spain. e-mail: rcamino@ugr.es, ES
Abstract: Let Ω be a smooth domain on the unit sphere 𝕊n whose closure is contained in an open hemisphere and denote by ℋ the mean curvature of ∂Ω as a submanifold of Ω with respect to the inward unit normal. It is proved that for each real number H that satisfies inf ℋ > − H ≥ 0, there exists a unique radial graph on Ω bounded by ∂Ω with constant mean curvature H. The orientation on the graph is based on the normal that points on the opposite side as the radius vector. Received: 5 June 2001 / Revised version: 9 April 2002 Research partially supported by a DGICYT Grant No. BFM2001-2967. Mathematics Subject Classification (2000): 53A10, 53C42, 49Q05, 49Q10
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