The min-max eigenvalue conjecture for the $p$-Laplacian

Let $1<p<\infty$, and let $\Delta_p$ denote the $p$-Laplacian of the oriented hypergraph under consideration. An eigenvalue is called a min-max eigenvalue if it is expressible in the min-max Rayleigh quotient form introduced above. Min-max eigenvalue conjecture. For $1<p<\infty$, all eigenvalues of $\Delta_p$ are min-max eigenvalues. The claim is known for the eigenvalues constructed by the stated min-max procedure, but it remains open whether these comprise all eigenvalues of the $p$-Laplacian; the analogous question is also open for graphs, domains, and manifolds.