A billiard-based game interpretation of the Neumann problem for the curve shortening equation. (English) Zbl 1170.35437

The authors developed a family of discrete games, whose value functions converge to the unique viscisity solution of the Neumann boundary problem of the curve shortening flow equation. It is to be noted that the Neumann boundary value problems of mean curvature flow equations can be intemately connected with purely deterministic game theory.


35K20 Initial-boundary value problems for second-order parabolic equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
91A05 2-person games