Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 x R
Identificadores
URI: https://hdl.handle.net/10481/82771Metadatos
Mostrar el registro completo del ítemEditorial
European Matematical Society
Fecha
2022-08-25Referencia bibliográfica
Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez, Slab theorem and halfspace theorem for constant mean curvature surfaces in H 2 ×R. Rev. Mat. Iberoam. 39 (2023), no. 1, pp. 307–320 DOI 10.4171/RMI/1372
Patrocinador
IMAG - María de Maeztu grant CEX2020-001105-M/ AEI/10.13039/501100011033, MICINN grant PID2020-117868GB-I00; Junta de Andalucía grants A-FQM-139-UGR18 and P18-FR4049.Resumen
We prove that a properly embedded annular end of a surface in H 2 ×R with constant mean curvature 0 < H≤ 1 / 2 0<H≤1/2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1 / 2 0<H≤1/2 contained in H2 × [ 0 , + ∞ ) H 2 ×[0,+∞) and with finite topology is necessarily a graph over a simply connected domain of H 2 H 2 . For the case H = 1 / 2 H=1/2, the graph is entire.