The Infinity-Potential in the Square

A representation formula for the solution of the $\mathrm{\infty }$-Laplace equation is constructed in a punctured square, the prescribed boundary values being $u=0$ on the sides and $u=1$ at the centre. This so-called $\mathrm{\infty }$-potential is obtained with a hodograph method. The heat equation is used and one of Jacobi’s Theta functions appears. The formula disproves a conjecture.