Generic Regularity of Minimal Submanifolds

Abstract: The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on minimal hypercones. It was conjectured that generically they can be perturbed away. In this talk, we shall present a way to resolve these singularities by perturbing metric in an 8-manifold and hence obtain smoothness under a generic metric. We shall also talk about certain generalizations of this generic smoothness of minimal submanifold in other dimensions and codimensions as well as their applications.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

---

NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

---