How to Define an Inverse Mean Curvature Flow Coming Out of Crystals?

This lecture explores the concept of inverse mean curvature flow (IMCF) in both smooth and weak solution contexts, with a focus on extending these mathematical tools to crystal growth modeling. Begin with a review of classical IMCF solutions from Huisken and Ilmanen's work and their application to the Riemannian Penrose inequality. Then discover how these traditional weak solution approaches fail in lower regularity settings needed for crystal modeling, which requires an anisotropic framework without additional regularity or ellipticity requirements. Learn how the speaker and collaborators developed a novel weak IMCF formulation that can effectively handle Lipschitz-regular objects like crystals. The presentation draws from joint research with Salvador Moll and Marcos Solera, delivered by Esther Cabezas-Rivas from the University of Valencia at the Institut des Hautes Etudes Scientifiques (IHES).