Project Title: Topics in nonlinear analysis and ergodic theory on uniformly convex geodesic spaces

Project Code: PN-II-RU-PD-2012-3-0152

Contract: 5/23.04.2013 financed by the Romanian Ministry of Education, CNCS - UEFISCDI

Period: May 2013 - October 2015

Members: Adriana Nicolae (Project Director) and Laurenţiu Leuştean (Mentor)

Host institution: Simion Stoilow Institute of Mathematics of the Romanian Academy

Abstract:

Geodesic spaces have become an important framework for the study of problems from various areas of mathematics with important applications. However, there are many concepts and results from the linear setting for which analogues in the geodesic context are still unknown. We address the study of regularity properties of geodesic spaces with a special focus on uniformly convex ones aiming to extend the theory of less regular frameworks than those normally considered in nonlinear analysis and ergodic theory and to apply the findings to specific problems in these fields. Proof mining techniques will also be applied to obtain effective bounds for different types of results in nonlinear analysis and ergodic theory.

Expected results:

Further study of:

• regularity properties of geodesic spaces
• the asymptotic behavior of nonlinear iterations in geodesic spaces
• ergodic theorems in uniformly convex geodesic spaces