Fritz Hiesmayr - A rigidity theorem for the Allen-Cahn equation in $S^3$

Tuesday, September 22, 2020 - 13:00
Speaker Information
Fritz Hiesmayr
UCL

Notes

We present a recent rigidity theorem for the Allen-Cahn equation in the three-sphere: critical points with Morse index are symmetric and vanish on a Clifford torus. One key ingredient is a novel Frankel-type property we establish for the nodal sets of any two distinct solutions: they intersect if they are connected. This in fact holds in all manifolds with positive Ricci curvature. Time permitting we will discuss additional rigidity results in higher-dimensional spheres.

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