09:30-10:30 Tuesday, 1 April 2025 Auditorium, Rectorate
Abstract
Minimal surfaces have represented for decades the classical mathematical model for thin material structures in equilibrium subject to surface tension (e.g. soap films). By neglecting the intrinsic three-dimensional nature of such structures, this model fails at capturing some of the physical properties observed in experiments. In this talk, I will take this point of view and show how a suitable version of the classical Plateau’s problem can be recast as the singular limit of a family of minimisation problems defined in terms of Gauss’ free energy in capillarity theory under an additional spanning constraint. I will discuss existence of minimisers, and explain what we know about their regularity and their geometry. Based on joint works of the speaker with King and Maggi (UT Austin), and with Bevilacqua and Velichkov (U Pisa).