14:30-15:30 Monday, 31 March 2025 Auditorium, Rectorate
Abstract
One of the earliest successes in the field of geometric flows is the complete description of the evolution by curvature of planar curves: every simple closed planar curve becomes convex and then shrinks to a round point in finite time (Grayson’s Theorem, ‘87). Since Polden’s PhD thesis in the late 1990s, gradient flows of energies for curves represented by geometric integrals involving curvature have gained popularity, and several higher-order flows have been proposed and studied in the literature. The proofs of global existence and long-term behavior of solutions rely on increasingly technical estimates but share core ideas. A key question is whether there is common ground in analyzing these gradient flows that leads to well-posedness and global existence of solutions. I will address this question by proposing a comprehensive approach to higher-order flows based on a generalization of the Gagliardo-Nirenberg inequality. Joint work with Luca Benatti.