Heteroclinic solutions and a Morse-theoretic approach to an Allen-Cahn approximation of mean curvature flows

Início: 06/10/2023 17:00

Término: 06/10/2023 18:00

Palestrante: Pedro Gaspar (Pontificia Universidad Católica de Chile)

E-mail do Palestrante: pedro.gaspar@mat.uc.cl

Resumo: The Allen–Cahn equation is a semilinear parabolic partial differential equation that models phase-transition and phase-separation phenomena and which provides a regularization for the mean curvature flow (MCF), one of the most studied extrinsic geometric flows. In this talk, we employ Morse-theoretical considerations to construct eternal solutions of the Allen–Cahn equation that connect unstable equilibria in compact manifolds. We describe the space of such solutions in a round 3-sphere under a low-energy assumption, and indicate how these solutions could be used to produce geometrically interesting MCFs. This is joint work with Jingwen Chen (University of Pennsylvania).