We provide an isoperimetric comparison theorem for small volumes in an n-dimensional Riemannian m... more We provide an isoperimetric comparison theorem for small volumes in an n-dimensional Riemannian manifold (M n , g) with C 3 bounded geometry in a suitable sense involving the scalar curvature function. Under C 3 bounds of the geometry, if the supremum of scalar curvature function S g < n(n − 1)k 0 for some k 0 ∈ R, then for small volumes the isoperimetric profile of (M n , g) is less then or equal to the isoperimetric profile of the complete simply connected space form of constant sectional curvature k 0. This work generalizes Theorem 2 of [12] in which the same result was proved in the case where (M n , g) is assumed to be compact. As a consequence of our result we give an asymptotic expansion in Puiseux series up to the 2nd nontrivial term of the isoperimetric profile function for small volumes, generalizing our earlier asymptotic expansion [29]. Finally, as a corollary of our isoperimetric comparison result, it is shown that for small volumes the Aubin-Cartan-Hadamard's conjecture is true in any dimension n in the special case of manifolds with C 3 bounded geometry, and S g < n(n − 1)k 0. Two different intrinsic proofs of the fact that an isoperimetric region of small volume is of small diameter. The 1st under the assumption of mild bounded geometry, that is, positive injectivity radius and Ricci curvature bounded below. The 2nd assuming the existence of an upper bound
Mediante el presente anexo, Generali Colombia Vida Compañía de Seguros S.A., en adelante la Compa... more Mediante el presente anexo, Generali Colombia Vida Compañía de Seguros S.A., en adelante la Compañía, asegura los servicios de asistencia, contenidos en las siguientes condiciones: PRIMERA: OBJETO DEL ANEXO EN VIRTUD DEL PRESENTE ANEXO, LA COMPAÑÍA GARANTIZA LA PUESTA A DISPOSICIÓN DEL AFILIADO DE UNA AYUDA MATERIAL INMEDIATA, EN FORMA DE PRESTACIÓN DE SERVICIOS, CUANDO ÉSTE SE ENCUENTRE EN DIFICULTADES, DE ACUERDO CON LOS TÉRMINOS Y CONDICIONES CONSIGNADOS EN EL PRESENTE ANEXO Y POR HECHOS DERIVADOS DE LOS RIESGOS ESPECIFICADOS EN EL MISMO.
We provide an isoperimetric comparison theorem for small volumes in an n-dimensional Riemannian m... more We provide an isoperimetric comparison theorem for small volumes in an n-dimensional Riemannian manifold (M n , g) with C 3 bounded geometry in a suitable sense involving the scalar curvature function. Under C 3 bounds of the geometry, if the supremum of scalar curvature function S g < n(n − 1)k 0 for some k 0 ∈ R, then for small volumes the isoperimetric profile of (M n , g) is less then or equal to the isoperimetric profile of the complete simply connected space form of constant sectional curvature k 0. This work generalizes Theorem 2 of [12] in which the same result was proved in the case where (M n , g) is assumed to be compact. As a consequence of our result we give an asymptotic expansion in Puiseux series up to the 2nd nontrivial term of the isoperimetric profile function for small volumes, generalizing our earlier asymptotic expansion [29]. Finally, as a corollary of our isoperimetric comparison result, it is shown that for small volumes the Aubin-Cartan-Hadamard's conjecture is true in any dimension n in the special case of manifolds with C 3 bounded geometry, and S g < n(n − 1)k 0. Two different intrinsic proofs of the fact that an isoperimetric region of small volume is of small diameter. The 1st under the assumption of mild bounded geometry, that is, positive injectivity radius and Ricci curvature bounded below. The 2nd assuming the existence of an upper bound
Mediante el presente anexo, Generali Colombia Vida Compañía de Seguros S.A., en adelante la Compa... more Mediante el presente anexo, Generali Colombia Vida Compañía de Seguros S.A., en adelante la Compañía, asegura los servicios de asistencia, contenidos en las siguientes condiciones: PRIMERA: OBJETO DEL ANEXO EN VIRTUD DEL PRESENTE ANEXO, LA COMPAÑÍA GARANTIZA LA PUESTA A DISPOSICIÓN DEL AFILIADO DE UNA AYUDA MATERIAL INMEDIATA, EN FORMA DE PRESTACIÓN DE SERVICIOS, CUANDO ÉSTE SE ENCUENTRE EN DIFICULTADES, DE ACUERDO CON LOS TÉRMINOS Y CONDICIONES CONSIGNADOS EN EL PRESENTE ANEXO Y POR HECHOS DERIVADOS DE LOS RIESGOS ESPECIFICADOS EN EL MISMO.
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