A real variable characterization of Gromov hyperbolicity of flute surfaces

23 pages, 1 figure.-- MSC2000 codes: 41A10, 46E35, 46G10.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.0093Previously presented as Communication at International Congress of Mathematicians 2006 (ICM2006, Madrid, Spain, Aug 22-30, 2006).Preaccepted for publication at: Osaka Journal of MathematicsIn this paper we give a characterization of the Gromov hyperbolicity of trains (a large class of Denjoy domains which contains the flute surfaces) in terms of the behavior of a real function. This function describes somehow the distances between some remarkable geodesics in the train. This theorem has several consequences; in particular, it allows to deduce a result about stability of hyperbolicity, even though the original surface and the modified one are not quasi-isometric.Research partially supported by three grants from M.E.C. (MTM 2006-11976, MTM 2006-13000-C03-02 and MTM 2007-30904-E), Spain.No publicad

The role of funnels and punctures in the Gromov hyperbolicity of Riemann surfaces

27 pages, no figures.-- MSC2000 codes: 30F20, 30F45.MR#: MR2243795 (2007e:30063)Zbl#: Zbl 1108.30031We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface S* obtained by deleting a closed set from one original surface S. In the particular case when the closed set is a union of continua and isolated points, the results clarify the role of punctures and funnels (and other more general ends) in the hyperbolicity of Riemann surfaces.Research by all three authors partially supported by a grant from DGI (BFM 2003-04870), Spain. In addition, research by third author (Eva Tourís) was partially supported by a grant from DGI (BFM 2000-0022), Spain.Publicad

Assessment of heritage rammed-earth buildings. The Alcázar of King Don Pedro I (Spain).

The conservation and maintenance of earthen buildings is crucial, especially when dealing with heritage sites. This normally involves considerable effort in preliminary studies, which must be well planned in order to efficiently manage any restoration. This case study proposes a methodology to briefly assess the current state of a historical rammed-earth wall, to bring to light specific information regarding approaches for subsequent studies or decisions. This methodology is based on the study of damage and risk as a tool to swiftly discern critical areas or issues needing immediate attention. The procedure is illustrated on an outstanding heritage building: the Alcázar of King Don Pedro I in Carmona (Seville, Spain). Our conclusions confirm that this methodology constitutes an efficient and straightforward means to obtain not only a preliminary assessment of rammed-earth walls, but also objective and useful criteria for decision-makers