GSCRM
Elliptic Submanifolds in Hyperbolic Geometry
| Coordinatore | Consorci Centre de Recerca Matematica
Organization address
address: FACULTAD CIENCIES UAB APRATADO 50 contact info |
| Nazionalità Coordinatore | Spain [ES] |
| Totale costo | 146˙717 € |
| EC contributo | 146˙717 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2009-IEF |
| Funding Scheme | MC-IEF |
| Anno di inizio | 2010 |
| Periodo (anno-mese-giorno) | 2010-10-01 - 2012-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
Consorci Centre de Recerca Matematica
Organization address
address: FACULTAD CIENCIES UAB APRATADO 50 contact info |
ES (BELLATERRA) | coordinator | 146˙717.00 |
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Obiettivo del progetto (Objective)
'This project studies the application of analytical tools to the resolution of geometric problems. The geometric problems proposed to be studied arise from hyperbolic geometry and representation theory. More precisely, it is proposed to investigate hyperbolic ends and flat conformal structures (FCSs). The former constitute an important part of the study of hyperbolic manifolds in general, since they arise when the Nielsen Kernel (which is bounded) is removed from a (convex, co-compact) hyperbolic manifold, nonetheless, the structure of the moduli space of hyperbolic ends as well as its compactification remains to be understood. Part of this project is devoted to the study of this problem. The latter arise as a natural geometric structure in the theory of representations. They are intimitely related to hyperbolic ends, but the properties of this identification remain to be fully understood, and part of the project is devoted to the resolution of this problem. This should also yield geometric structures on the moduli space of FCSs. Finally, in the two dimensional case, these structures yield continuous curves inside the moduli space of FCSs, whose geometric properties we propose to investigate. The tools used are mostly immersed submanifolds satisfying elliptic conditions, such as constant curvature. In particular, it is proposed to use a new concept of curvature, developed by the applicant, called special Lagrangian (SL) curvature, which captures the important convexity properties of Gaussian curvature whilst overcoming its technical limitations. In order to fully realise the potential of SL curvature as a geometric tool, various properties (especially compactness) remain to be fully understood, to which the final part of the project is devoted.'