Séminaire Cirget: «The determination of a shrinking Ricci soliton from its geometry at infinity»
Conférencier: Brett Kotschwar, Arizona State University
Résumé/Abstract: Shrinking solitons are self-similar solutions to the Ricci flow and models for the geometry of a solution near a developing singularity. The geometric behavior of a complete noncompact shrinking soliton near infinity is highly constrained; in dimension four, it has been conjectured that every such soliton is either smoothly asymptotic to a cone or to a (quotient of) a generalized cylinder. I will describe some uniqueness results, obtained jointly with Lu Wang, which demonstrate the extent to which a shrinking soliton is determined by its asymptotic geometry, and discuss their application to the classification problem in dimensions four and higher.
Date / heure
- Département de mathématiques
- Centre interuniversitaire de recherches en géométrie et topologie (CIRGET)