Hierarchy structures in finite index CMC surfaces Meeks III, William H. Pérez Muñoz, Joaquín Constant mean curvature Finite index H-surfaces Area estimates for constant mean curvature surfaces Curvature estimates for one-sided stable minimal surfaces William H. Meeks, III was partially supported by CNPq, Brazil, grant no. 400966/2014-0. Research of both authors was partially supported by MINECO/MICINN/FEDER grant nos. PID2020-117868GB-I00 and CEX2020-001105-M, both funded by MCINN/AEI, and by regional grant no. P18-FR-4049 funded by Junta de Andalucia. Given epsilon(0) > 0, I is an element of N boolean OR {0} and K 0, H 0 >= 0, let X be a complete Riemannian 3-manifold with injectivity radius Inj(X) = e 0 and with the supremum of absolute sectional curvature at most K-0, and let M (sic) X be a complete immersed surface of constant mean curvature H is an element of [ 0, H-0] with index at most I. For such M (sic) X, we prove a structure theorem which describes how the interesting ambient geometry of the immersion is organized locally around at most I points of M, where the norm of the second fundamental form takes on large local maximum values. 2023-09-19T08:17:45Z 2023-09-19T08:17:45Z 2023-07-26 info:eu-repo/semantics/article Meeks III, William H. and Pérez, Joaquín. "Hierarchy structures in finite index CMC surfaces" Advances in Calculus of Variations, 2023. [https://doi.org/10.1515/acv-2022-0113] https://hdl.handle.net/10481/84492 10.1515/acv-2022-0113 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Walter de Gruyter GmbH