Fractional Convexity

Explore a groundbreaking lecture on fractional convexity, extending the traditional concept of convexity in Euclidean space to a fractional setting. Delve into the study of fractional convex envelopes within domains, examining their characterization as viscosity solutions to non-local equations involving the infimum of one-dimensional fractional Laplacians across all possible directions. Discover the relationship between these solutions and those of the fractional Monge-Ampere equation. Learn about collaborative research findings with J. Rossi (UBA) and A. Quaas (USM) in this 40-minute talk presented at the Hausdorff Center for Mathematics.