Every entire C² solution u:ℝ⁸→(−1,1) of Δu=u³−u with a strictly positive derivative in one fixed direction is a planar tanh heteroclinic, without an assumed limit at either end of that direction.
Every entire C² solution u:ℝ⁸→(−1,1) of Δu=u³−u with a strictly positive derivative in one fixed direction is a planar tanh heteroclinic, without an assumed limit at either end of that direction.
Every entire C² solution u:ℝ⁸→(−1,1) of Δu=u³−u with a strictly positive derivative in one fixed direction is a planar tanh heteroclinic, without an assumed limit at either end of that direction.
If correct, resolves the remaining dimension-eight monotone rigidity case of De Giorgi’s conjecture for the scalar quartic Allen–Cahn equation.
Are all bounded strictly monotone Allen–Cahn solutions in ℝ⁸ planar?
Publication dates and editorial changes.
OpenAI reports a positive solution to De Giorgi’s conjecture in dimension eight
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
