ERC Starting Grant · 2024
Minimal submanifolds in Arbitrary Geometries as Nodal sEts: Towards hIgher Codimension
The goal of this research proposal is to advance the calculus of variations of area in codimension higher than one, specifically existence and regularity of its critical points (minimal submanifolds) and properties of its gradient flow (mean curvature flow). These are central objects in mathematics since three centuries and contributed to the birth of geometric analysis, geometric measure theory, and calculus of variations. Their (non-)existence often reveals deep links between small-scale geometry (curvature) and large-scale structure (topology). While the hypersurface case is by now well understood, with several deep results in the last two decades, very little is known in codimension at…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.