Entropies of non-positively curved metric spaces

We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform packing condition. Similar estimates will be given in case of closed subsets of the boundary of Gromov-hyperbolic metric spaces with convex geodesic bicombings

Entropies of non positively curved metric spaces

We show the equivalences of several notions of entropy, such as a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform packing condition. Similar estimates will be given in case of closed subsets of the boundary of Gromov-hyperbolic metric spaces with convex geodesic bicombings. A uniform Ahlfors regularity of the limit set of quasiconvex-cocompact actions on Gromov-hyperbolic packed metric spaces with convex geodesic bicombing will be shown, implying a uniform rate of convergence to the entropy. As a consequence we prove the continuity of the critical exponent for quasiconvex-cocompact groups with bounded codiameter

GH-convergence of CAT(0)(0)-spaces: stability of the Euclidean factor

We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\infty$, then the dimension of the maximal Euclidean factor splitted off by $X_\infty$ and $X_j$ is the same, for $j$ big enough. In other words, no additional Euclidean factors can appear in the limit.Comment: arXiv admin note: text overlap with arXiv:2307.0564

Ahlfors regular conformal dimension and Gromov-Hausdorff convergence

We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. A corollary is the upper semicontinuity of the Ahlfors regular conformal dimension of limit sets of discrete, quasiconvex-cocompact group of isometries of uniformly bounded codiameter of $\delta$-hyperbolic metric spaces under equivariant pointed Gromov-Hausdorff convergence of the spaces.Comment: Minor revision

Packing conditions in metric spaces with curvature bounded above and applications

General metric spaces satisfying weak and synthetic notions of upper and lower curvature bounds will be studied. The relations between upper and lower bounds will be pointed out, especially the interactions between a packing condition and different forms of convexity of the metric. The main tools will be a new and flexible definition of entropy on metric spaces and a version of the Tits Alternative for groups of isometries of the metric spaces under consideration. The applications can be divided into classical and new results: the former consist in generalizations to a wider context of the theory of negatively curved Riemannian manifolds, while the latter include several compactness and continuity results

Desafíos de la negociación de cambio climático desde la perspectiva de Ecuador

El presente ensayo se enfoca en identificar y comentar las principales debilidades que pueden evidenciarse dentro del potencial negociador del Ecuador, en especial, con respecto a la gestión del cambio climático. Dichas debilidades se ven agravadas por el hecho de que el Ecuador es un país en desarrollo, por lo que presenta múltiples temas a negociar, temas trascendentes para el desarrollo social, político y económico de su colectivo nacional. Los principales retos pueden identificarse en la falta de preparación técnica en las mayores herramientas negociadoras según las directrices de la Escuela de Harvard; el escaso conocimiento del idioma inglés técnico, de los principales mecanismos comunicacionales y de oratoria, a lo que suma la falta de continuidad en los equipos negociadores, los que son sistemáticamente rotados

La negociación como herramienta de comunicación en un mundo de relativismo y subjetividad

La negociación, antes que ser una herramienta de trabajo dirigida a la resolución de conflictos y a la consecución de acuerdos, se caracteriza por una componente fundamental, a veces desestimada o del todo ignorada: el hecho que obliga a un previo proceso de introspección y de autoanálisis, lo que finalmente facilita el proceso de comunicación con nuestro entorno

Convergence and collapsing of CAT(0)(0)-group actions

We study the theory of convergence for groups $\Gamma$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces $X$, and for their quotients $M=\Gamma \backslash X$ (CAT$(0)$-orbispaces). We describe splitting and collapsing phenomena for nonsingular actions, explaining how they occurs and when the limit action is discrete. This leads to finiteness results for nonsingular actions on uniformly packed CAT$(0)$-spaces with uniformly bounded codiameter, which generalize and sharpen, in nonpositive curvature, the classical finiteness theorems of Riemannian geometry. Finally, we prove some closure and compactness theorems in the class of CAT$(0)$-homology orbifolds, and an isolation result for flats