A two-player zero-sum probabilistic game that approximates the mean curvature flow

TL;DR

This paper introduces a novel two-player zero-sum game involving probability that approximates the mean curvature flow of hypersurfaces, providing a new connection between game theory and geometric evolution equations.

Contribution

The paper presents a new probabilistic game model that approximates mean curvature flow, bridging geometric PDEs and stochastic game theory.

Findings

The game accurately approximates mean curvature flow.

The approach involves symmetric rules and probabilistic elements.

Potential applications in geometric analysis and numerical simulations.

Abstract

In this paper we introduce a new two-player zero-sum game whose value function approximates the level set formulation for the geometric evolution by mean curvature of a hypersurface. In our approach the game is played with symmetric rules for the two players and probability theory is involved (the game is not deterministic).