Mapping Riemannian Manifolds in Metric Spaces
Explore the fascinating world of Riemannian manifolds and their mappings in metric spaces through this 56-minute mathematics colloquium talk. Delve into the importance of special maps, such as isometric, harmonic, and area minimizing, in understanding the geometry of Riemannian manifolds. Survey various special mappings and their applications in systolic geometry, inverse problems, and dynamical systems. Discover new insights into stability problems for geometric inequalities and the construction of canonical shapes for manifolds. Follow the speaker's journey through topics including isometry, concrete metrics, global isometries, harmonic maps, minimal maps, and compactness theorems. Gain a deeper understanding of how these concepts contribute to the broader field of mathematics and their practical implications in solving complex geometric problems.