Bi-Lipschitz regularity of 2-varifolds with the critical Allard condition

Abstract: For an integral 2-varifold in the unit ball of the Euclidean space passing through the origin, if it satisfies the critical Allard condition, i.e., the mass of the varifold in the unit ball is close to the area of a flat unit disk and the L$^2$ norm of the generalized mean curvature is small enough, we show that locally the support of the varifold admits a bi-Lipschitz parameterization from the unit disk. The presentation is based on a joint work with Dr. Yuchen Bi.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

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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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