Abstract: Motivated by recent developments on the connections between the Allen-Cahn equation – which is ubiquitous in certain models of phase transitions and separation phenomena – and minimal hypersurfaces, we will discuss variational and geometric properties of low energy solutions to certain PDEs in the sphere and other symmetric domains. Furthermore, we will describe a geometric bifurcation result for solutions of the Allen-Cahn equation in the 3-sphere and point out some relations with the variational theory of minimal surfaces.
This is joint work with Rayssa Caju, Marco Guaraco and Henrik Matthiesen.
Date: Apr 22, 2021 at 16:15 h
Venue: Modalidad online vía Zoom
Speaker: Pedro Gaspar
Affiliation: The University of Chicago, USA.
Coordinator: Natham Aguirre