Preservation of geometrical properties under sphericalization and flattening in the metric setting

ABSTRACT:

The process of obtaining the Riemann sphere from the complex  plane, and viceversa, was generalized in the metric setting by using sphericalization and flattening. These conformal transformations are  dual to each other, and the performance of sphericalization followed by
flattening, or viceversa, results in a metric space that is bi-Lipschitz  equivalent to the original space. A very natural problem is therefore to study which geometric properties are preserved under these  transformations.
Metric spaces endowed with a doubling measure and supporting a Poincaré  inequality are nowadays considered a standard class of spaces when developing a first order differential analysis in a metric measure space  setting. In this talk we will focus on the preservation, under
sphericalization and flattening, of several geometrical properties,  including Poincaré inequalities. The talk is based on a joint work with Xining Li

Posted on May 27, 2016 in Optimization and Equilibrium, Seminars