Revista De La Union Matematica Argentina 

About: Revista De La Union Matematica Argentina is an academic journal published by Unión Matemática Argentina. The journal publishes majorly in the area(s): Mathematics & Lie group. It has an ISSN identifier of 0041-6932. It is also open access. Over the lifetime, 680 publications have been published receiving 3326 citations. The journal is also known as: Revista - Unión Matemática Argentina (1968).

A short survey on biharmonic maps between Riemannian manifolds

Abstract: and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively. More precisely: • biharmonic maps are the critical points of the bienergy functional E2 : C∞(M,N) → R, E2(φ) = 12 ∫

Metallic structures on Riemannian manifolds

Abstract: Our aim in this paper is to focus on some applications in differential geometry of the metallic means family (a generalization of the golden mean) and generalized Fibonacci sequences, using a class of polynomial structures defined on Riemannian manifolds. We search for properties of the induced structure on a submanifold by metallic Riemannian structures and we find a necessary and sufficient condition for a submanifold to be also a metallic Riemannian manifold in terms of invariance. Also, the totally geodesic, minimal and respectively totally umbilical hypersurfaces in metallic Riemannian manifolds are analyzed and the Euclidean space and its hypersphere is treated as example.

Entire solutions of the allen-cahn equation and complete embedded minimal surfaces

Abstract: We review some recent results on construction of entire solutions to the classical semilinear elliptic equation ∆u+u−u = 0 in R . In various cases, large dilations of an embedded, complete minimal surface approximate the transition set of a solution that connects the equilibria ±1. In particular, our construction answers negatively a celebrated conjecture by E. De Giorgi in dimensions N ≥ 9.

Tensor categories: a selective guided tour

Abstract: These are the, somewhat polished and updated, lecture notes for a three hour course on tensor categories, given at the CIRM, Marseille, in April 2008. The coverage in these notes is relatively non-technical, focusing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of the experts will find something interesting in them. Once the basic definitions are given, the focus is mainly on categories that are linear over a field k and have finite dimensional hom-spaces. Connections with quantum groups and low dimensional topology are pointed out, but these notes have no pretension to cover the latter subjects to any depth. Essentially, these notes should be considered as annotations to the extensive bibliography. We also recommend the recent review, which covers less ground in a deeper way.

Infinite dimensional homogeneous reductive spaces

Abstract: Let A . be a Banach algebr a and AX the group of invertible elements of A. A general setting for the theory of homogeneous reductive Sflaces Q over AX is presented. Also, in the case where A is a C*-algebra, we present the notion of an involution in Q. The differential geometry associated to such spaces is developed . 1 Introduct ion. Let A b e a ;Banach algebra and AX the group of invertible elements of A . Several examples of homogeneous reductive spaces (see9 , 1 0 for the definitions in the finite dimensional case) with group AX , are studied in1 ,3 ,4 , 5 , 6 , 13 . In the case where A is a C* -algebra, these spaces present a natural involution and a Finsler structure . Metric properties of these spaces are studied in the mentioned articles-and are based on results of2,8 ,16 . We present here some b asic results , of a theory, where the aforementioned examples find a natural treatment . We also present the concept of the classifying con n e ction on homogeneous reductive spaces and show some of its properties (section 6) . We study the general concept of involution in a homogeneous reductive space in the case when A is a C*-algebra and , in connection with it , we define the notion of regularity. The main result in relation with the idea of regularity is Theorem 10 . 1 . The ·hypothesis of regularity has been verified in all finite dimensional cases and some infinite dimensional ones (see7 ) . Some of these results were presented in the \"Tercera Escuela Venezolana de Matematicas\" , Merida 1990 , see12 . The general setting for this theory, ap­ peared for the first time in the preprint13 which was submitted for publication in Acta Cientifica Ven ezolana . The last part of this preprint studies the Space of representations of a compact Lie Group on a C*-algebra as an example for 103