# Local and global structure of metric measure spaces with Ricci curvature lower bounds

Main funder

Funder's project number: 274372

Funds granted by main funder (€)

- 434 485,00

Funding program

- Research post as Academy Research Fellow, AoF (Academy of Finland)

Project timetable

Project start date: 01/09/2014

Project end date: 31/08/2019

Summary

The project is in the area of pure mathematics. More precisely, it is in the areas of differential geometry, geometric function theory and geometric measure theory. Aim of the project is to investigate the local and global properties of metric measure spaces with Ricci curvature lower bounds as introduced by Lott, Sturm and Villani. The project also studies the more strict definition of Riemannian Ricci curvature lower bounds by Ambrosio, Gigli and Savaré. The curvature bounds are based on optimal mass transportation. The study of these abstract notions of curvature bounds will also increase our knowledge on Riemannian manifolds with Ricci curvature bounded below, as well as their Gromov-Hausdorff limits.

Principal Investigator

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