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A Delaunay-type
classification result for prescribed mean curvature surfaces
in $\mathbb{M}^2(\kappa)\times\mathbb R$
Antonio Bueno |
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Vol. 313 (2021), No. 1, 45–74
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DOI: 10.2140/pjm.2021.313.45
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Abstract |
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The purpose of this paper is to study immersed surfaces in the product spaces , whose mean curvature is given as a function depending on their angle function. This class of surfaces extends widely, among others, the well-known theory of surfaces with constant mean curvature. In this paper we give necessary and sufficient conditions for the existence of prescribed mean curvature spheres, and we describe complete surfaces of revolution proving that they behave as the Delaunay surfaces of CMC type. |
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Keywords
prescribed mean curvature, product space, rotational
surface, existence of spheres, Delaunay-type classification
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Mathematical Subject Classification 2010
Primary: 34C05, 34C40, 53A10, 53C42
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Milestones
Received: 17 June 2019
Revised: 4 January 2021
Accepted: 16 April 2021
Published: 17 September 2021
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Authors |
| Antonio Bueno | |
| Departamento GeometrĂa y
TopologĂa Universidad de Granada E-18071 Granada Spain |
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