Summary: Given an \(\infty\)-harmonic function \(u_{\infty}\) on a domain \(\Omega \subseteq \mathbb{R}^2\), consider the function \(w=-\log |\nabla u_{\infty}|\). If \(u_{\infty}\in C^2 (\Omega)\) with \(\nabla u_{\infty} \neq 0\) and \(\nabla |\nabla u_{\infty}|\neq 0\), then it is easy to check that

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the streamlines of \(u_{\infty}\) are the level sets of \(w\) and

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\(w\) solves the level set formulation of the inverse mean curvature flow.

For less regular solutions, neither statement is true in general, but even so, \(w\) is still a weak solution of the inverse mean curvature flow under far weaker assumptions. This is proved through an approximation of \(u_{\infty}\) by \(p\)-harmonic functions, the use of conjugate \(p'\)-harmonic functions, and the known connection of the latter with the inverse mean curvature flow. A statement about the regularity of \(|\nabla u_{\infty}|\) arises as a by-product.