A regularity theorem for area-minimizing currents at higher multiplicity boundary points

Abstract: The boundary regularity theory for area-minimizing integral currents in higher codimension has been completed in 2018 by a work of De Lellis, De Philippis, Hirsch and Massaccesi proving the density of regular boundary points. In this talk, I will present our recent paper where we took a first step into analyzing area-minimizing currents with higher multiplicity boundary. This question has first been raised by Allard and later again by White. We focus on two-dimensional currents with a convex barrier and define the regular boundary points to be those around which the current consists of finitely many regular submanifolds meeting transversally at the boundary. Adapting the techniques of Almgren, we proved that every boundary point is regular in the above sense. This is a joint work with C. De Lellis and S. Nardulli.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper )

Comments: Get-together (30 min) $\cdot$ presentation Simone Steinbrüchel (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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