FALL 2020 Nonlinear Analysis Seminar Series

Assistant Professor Armin Schikorra, University of Pittsburgh

Title: Scale-invariant tangent-point energies for knots and fractional harmonic maps

Abstract:

I will report about the theory of minimizing and critical knots under a set of scale invariant knot energies, the so-called tangent-point energy. We obtain lower semicontinuity and weak Sobolev-convergence of minimizing sequences to critical points away from finitely many points in the domain. Extending earlier work on Moebius-, and O'Hara energies we also obtain regularity for such critical points. This is based on joint work with S. Blatt, Ph. Reiter, and N. Vorderobermeier.

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