Singular solutions to variational problems and to partial differential equations arise naturally in several contexts, both in Pure Mathematics and in the Applied Sciences. Among these, the Theory of Minimal Surfaces and the study of Mean Curvature Flows have represented a paradigm for decades, fostering the development of several tools and techniques in Analysis and Geometry and laying the foundations of Geometric Measure Theory.
Building on previous work by the PI, this project aims at developing a set of robust analytical techniques able to provide a unified understanding of the properties (size, fine geometric structure, dynamics) of the singular structures exhibited by physical systems governed by surface tension, and at exploring their range of applicability to several other nonlinear problems in Geometric Analysis, the Calculus of Variations, and PDE theory.