naa a22 4500 510810594 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9287-8 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9287-8 Nunes Ivaldo Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro-RJ, Brazil aut Rigidity of Area-Minimizing Hyperbolic Surfaces in Three-Manifolds [Elektronische Daten] [Ivaldo Nunes] We prove that if M is a three-manifold with scalar curvature greater than or equal to −2 and Σ⊂M is a two-sided compact embedded Riemann surface of genus greater than 1 which is locally area-minimizing, then the area of Σ is greater than or equal to 4π(g(Σ)−1), where g(Σ) denotes the genus of Σ. In the equality case, we prove that the induced metric on Σ has constant Gauss curvature equal to −1 and locally M splits along Σ. We also obtain a rigidity result for cylinders (I×Σ,dt 2+g Σ), where I=[a,b]⊂ℝ and g Σ is a Riemannian metric on Σ with constant Gauss curvature equal to −1. Mathematica Josephina, Inc., 2011 Minimal surfaces nationallicence Constant mean curvature surfaces nationallicence Scalar curvature nationallicence Rigidity nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1290-1302 1050-6926 23:3<1290 2013 23 12220 https://doi.org/10.1007/s12220-011-9287-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9287-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nunes Ivaldo Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro-RJ, Brazil aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1290-1302 1050-6926 23:3<1290 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer