caa a22 4500 445843845 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00526-010-0383-6 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0383-6 Parabolic stable surfaces with constant mean curvature [Elektronische Daten] [José Manzano, Joaquín Pérez, M. Rodríguez] We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrödinger operator −L=−(Δ +q) on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $${H\in \mathbb{R}}$$ in homogeneous spaces $${\mathbb{E} (\kappa ,\tau)}$$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $${\mathbb{H}^2\times \mathbb{R}}$$ , then $${|H|\leq \frac{1}{2}}$$ and if equality holds, then M is either an entire graph or a vertical horocylinder. Springer-Verlag, 2010 Manzano José Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain aut Pérez Joaquín Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain aut Rodríguez M. Departamento de Algebra, Universidad Complutense de Madrid, Madrid, Spain aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 137-152 0944-2669 42:1-2<137 2011 42 526 https://doi.org/10.1007/s00526-010-0383-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0383-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Manzano José Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain aut NATIONALLICENCE 700 1- Pérez Joaquín Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain aut NATIONALLICENCE 700 1- Rodríguez M. Departamento de Algebra, Universidad Complutense de Madrid, Madrid, Spain aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 137-152 0944-2669 42:1-2<137 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer