Analysis and Probability Seminar: “Fractional Sobolev Norms and BV Functions on Manifolds”

February 26, 2019 at 2:30 PM in Yost 306

Speaker: Andreas Kreuml (Vienna University of Technology)


We extend the notion of fractional Sobolev seminorms and fractional perimeters to compact Riemannian manifolds. The dependence of both of these functionals on a parameter 0 < s < 1 raises the question of convergence in the limit cases. For s tending to 1, their asymptotic behaviour can be modeled by a larger class of non-linear integral operators whose kernels concentrate on one point in the limit. In particular, the limit of fractional perimeters yields the classical perimeter functional which generalizes the notion of surface area to a broad class of sets.

This talk is based on joint work with Olaf Mordhorst (Vienna University of Technology).

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