# 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

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

Other persons related to this project (JYU)

Primary responsible unit

Fields of science

Related publications and other outputs

- Universal Infinitesimal Hilbertianity of Sub-Riemannian Manifolds (2023) Le Donne, Enrico; et al.; A1; OA
- Testing the Sobolev property with a single test plan (2022) Pasqualetto, Enrico; A1; OA
- A density result on Orlicz-Sobolev spaces in the plane (2021) Ortiz, Walter A.; et al.; A1; OA
- A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space (2020) Di Marino, Simone; et al.; A1; OA
- Indecomposable sets of finite perimeter in doubling metric measure spaces (2020) Bonicatto, Paolo; et al.; A1; OA
- Multi-marginal entropy-transport with repulsive cost (2020) Gerolin, Augusto; et al.; A1; OA
- Sharp estimate on the inner distance in planar domains (2020) Lučić, Danka; et al.; A1; OA
- Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces (2019) Gerolin, Augusto; et al.; A1; OA
- Nonexistence of Optimal Transport Maps for the Multimarginal Repulsive Harmonic Cost (2019) Gerolin, Augusto; et al.; A1; OA
- Removable sets for intrinsic metric and for holomorphic functions (2019) Kalmykov, Sergei; et al.; A1; OA