A structure theory for branched stable hypersurfaces

Abstract: There are few known general regularity results for stationary integral varifolds aside from Allard’s celebrated theory. The primary reason for this is the possibility of a degenerate type of singularity known as a branch point, where at the tangent cone level singularities vanish and are replaced with regions of higher multiplicity. In this talk I will discuss a recent regularity theory for branched stable hypersurfaces which do not contain certain so-called classical singularities, including new tangent cone uniqueness results in the presence of branch points. This theory can be readily applied to area minimising hypercurrents mod p, which resolves an old conjecture from the work of Brian White. Some results are joint with Neshan Wickramasekera.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper )

Comments: Get-together (30 min) $\cdot$ presentation Paul Minter (60 min) $\cdot$ questions and discussions (30 min).

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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).

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