How Curved are Level Sets of Solutions to Elliptic PDE? - Part 2

This lecture continues the exploration of level sets in solutions to elliptic partial differential equations, focusing on their curvature properties. Examine how the geometry of level sets in semilinear elliptic equations (δ(u) = f(u)) draws inspiration from Hamilton and Perelman's work on mean curvature flow and Ricci flow. Learn about fundamental tools in algebraic and differential geometry, including Jacobi functions and the Levi-Civita affine connection, while discovering potential applications to eigenfunction level sets. This second part of David Jerison's Zygmund Calderón Lectures in Analysis from MIT provides advanced mathematical insights, though viewers should note that due to technical difficulties, only partial video is available for approximately the first half, with the remainder being audio only.