Rigidity of Mass-Preserving 1-Lipschitz Maps from Integral Current Spaces into Euclidean Spaces

Explore a 42-minute conference talk from the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean spaces. Discover the proof that demonstrates how a 1-Lipschitz map from an n-dimensional integral current space onto the n-dimensional Euclidean ball, which preserves the mass of the current and is injective on the boundary, must be an isometry. Examine the implications of this result, including the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani. Gain insights into this joint work by Raquel Perales and G. Del Nin, presented as part of the ESI workshop in May 2024.