Title: A game-theoretic proof of convexity preserving properties for motion by curvature

Authors: Qing Liu, Armin Schikorra and Xiaodan Zhou

Issue: Volume 65 (2016), Issue 1, 171-197


In this paper, we revisit the convexity-preserving properties for the level set mean curvature flow equation by using the game-theoretic approximation established by Kohn and Serfaty (2006). Our new proofs are based on investigating game strategies or iterated applications of dynamic programming principles, without invoking deep partial differential equation theory. We also use this method to study convexity preserving for the Neumann boundary problem.