Second Order Mean-Curvature Flow as a Mean-Field Game

Explore the mathematical connection between second-order mean-curvature flow and mean-field games in this 40-minute conference talk. Learn how the second-order mean-curvature flow differs from the classical version, where acceleration rather than velocity is proportional to mean curvature, and discover why this creates significant analytical challenges. Understand the hyperbolic nature of the "cascade equation" that describes this flow and why traditional PDE methods fail due to the absence of the comparison principle. Examine the innovative approach that identifies solutions to the cascade PDE with minimal elements of value functions in mean-field games, enabling existence proofs through geometric measure theory techniques. Gain insights into the collaborative research demonstrating how tools from probability theory and geometric analysis can solve problems in differential geometry that resist conventional PDE approaches.