CRM: Centro De Giorgi
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A Pisan workshop in geometric analysis

Asymptotics of the fractional perimeter and existence of bounded harmonic functions on Riemannian manifolds

speaker: Michele Caselli (Scuola Normale Superiore)

abstract: I will describe some recent results on the asymptotics of the fractional s-perimeter of Riemannian manifolds, as s tends to zero. We will introduce the fractional Laplacian and fractional perimeter on complete (also non-compact) Riemannian manifolds, and I will show how our result generalizes the existing results on this asymptotics. Lastly, I will give some ideas on why this asymptotics detects the existence of bounded harmonic functions on the base manifold. This is joint work with Luca Gennaioli (SISSA).

Thu 21 Sep, 11:20 - 12:20, Aula Dini
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