Geometric inequalities and Optimal Transport in Riemannian Geometry

在这个项目的目的是研究等周不等式在黎曼和次黎曼流形变分方法，特别是通过数学理论的最佳运输。一个特殊的问题是下界里奇曲率的情况下，实际上是一个环境海森堡群的情况下。在任何一种情况下，分析归结为建立对周围空间的某些类型的测地线分解的控制，这允许减少问题的维度。该项目位于黎曼几何和几何分析的交叉点，需要深入了解几何和分析的广泛领域。

In this projects aims to investigate isoperimetric inequalities in Riemannian and subriemannian manifolds by variational methods, in particular by the mathematical theory of optimal transport. A particular question is the case of lower bounded Ricci curvature and indeed the case of an ambient Heisenberg group. In either case the analysis comes down to establishing control on certain types of geodesic decompositions of the ambient space, which allows for a reduction of the dimension of the problem. The project lies at the intersection of Riemannian geometry and Geometric analysis and requires deep understanding of wide areas in geometry and analysis.