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math.AP2017★ 11 cited
Allen-Cahn min-max on surfaces
Christos Mantoulidis
We use a min-max procedure on the Allen-Cahn energy functional to construct geodesics on closed, 2-dimensional Riemannian manifolds, as motivated by the work of Guaraco. Borrowing…
math.AP2017★ 2 cited
A note on the Morse index of 2k-ended phase transitions in R^2
Christos Mantoulidis
We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R^2 is >= k-1. This bound is expected to be sharp.