#### Vol. 313, No. 1, 2021

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A Delaunay-type classification result for prescribed mean curvature surfaces in $\mathbb{M}^2(\kappa)\times\mathbb R$

### Antonio Bueno

Vol. 313 (2021), No. 1, 45–74
DOI: 10.2140/pjm.2021.313.45
##### Abstract

The purpose of this paper is to study immersed surfaces in the product spaces ${\mathbb{𝕄}}^{2}\left(\kappa \right)×ℝ$, whose mean curvature is given as a ${C}^{1}$ 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.

##### Keywords
prescribed mean curvature, product space, rotational surface, existence of spheres, Delaunay-type classification
##### Mathematical Subject Classification 2010
Primary: 34C05, 34C40, 53A10, 53C42
##### Milestones
Received: 17 June 2019
Revised: 4 January 2021
Accepted: 16 April 2021
Published: 17 September 2021
##### Authors
 Antonio Bueno Departamento Geometría y Topología Universidad de Granada E-18071 Granada Spain