Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m

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Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces. (2009, unknown): “This conjecture”
ENERGY ESTIMATES AND 1-D SYMMETRY FOR NONLINEAR EQUATIONS INVOLVING THE HALF-LAPLACIAN (2010, methodology): “For equations of Allen-Cahn type involving the Laplacian, −∆u = f(u), saddle solutions have been studied in [7, 8].”
Stable solutions of the Allen–Cahn equation in dimension 8 and minimal cones (2011, background): “Let us mention that, in dimension n + 1 = 2m, with m ≥ 1, Cabré and Terra [10] have found solutions of the Allen-Cahn equation whose zero set is exactly given by the cone Cm,m.”