7 sep 2021 -- 14:00   [open in google calendar]

Abstract.

We introduce a notion of uniform convergence for local and nonlocal curvatures and we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of several nonlocal geometric evolutions. We study the limit of the s-fractional mean curvature flows as s tends to zero and s tends to one. Moreover, in analogy with s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as s tends to zero. Furthermore, using a suitable core-radius regularization, we define s-fractional perimeters and s-fractional curvatures also for s larger than one and we show that - as the core-radius vanishes - the corresponding geometric flows converge to the classical mean curvature flow. Eventually, we discuss the limit behavior of s-fractional heat flows as s tends to zero and one.