Introduction to Rectifiability in Metric Spaces - Lecture 3

Learn about geometric measure theory and n-rectifiable sets in this 59-minute mathematics lecture that explores how non-smooth sets can be parametrized using Lipschitz images of n-dimensional Euclidean space. Delve into the characterizations of rectifiable subsets in Euclidean space and their significant implications for partial differential equations, harmonic analysis, and fractal geometry. Explore recent developments in non-Euclidean metric spaces, focusing on new characterizations of rectifiable subsets through non-linear projections and tangent spaces. Master fundamental concepts and background knowledge necessary to understand geometric measure theory in both Euclidean and non-Euclidean settings.