In this very short post, we look at the properties of a certain bump function of the collection of all geodesic rays emanating from a fixed point 
towards irregular points on the geodesic boundary 
of a non-compact symmetric space
Notes on polar coordinates for symmetric spaces
In this short blog post, we are going to introduce a “coordinate system” on Riemannian symmetric spaces called polar coordinates, that arise as an immediate consequence of Cartan’s decomposition theorem. The quotation marks are due to the fact that we have some choice in how to express a point in these coordinates.
Continue reading “Notes on polar coordinates for symmetric spaces”The rigid world of symmetric spaces of noncompact type
The current post is based on a talk I gave at the university of Leiden which unfortunately I completely butchered due, in part, to the sudden realization that I had not chance to get through this material in the given time. Nothing here is new or proved, though some sketches are added when I find it relevant.
The (unattained) goal of the presentation was to show how much of the geometry of a symmetric space of noncompact type can be determined from it boundary sphere alone (in rank 1 cases) and a simplicial complex called the boundary at infinity (in higher rank cases) by following the evolution of the Mostow rigidity theorem from its origins (closed quotients of real hyperbolic spaces) to higher ranks.
Continue reading “The rigid world of symmetric spaces of noncompact type”