A game-theoretic proof of convexity preserving properties for motion by curvature Qingqing LiuArmin SchikorraXiaodan Zhou 49L2535J9335K9349N90convexity preservingcurvature flow equationsdiscrete gamesviscosity solutions 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. Indiana University Mathematics Journal 2016 text pdf 10.1512/iumj.2016.65.5740 10.1512/iumj.2016.65.5740 en Indiana Univ. Math. J. 65 (2016) 171 - 197 state-of-the-art mathematics http://iumj.org/access/