Stationary Integral Varifolds near Multiplicity 2 Planes

Abstract: A key open question in geometric measure theory concerns the optimal regularity conclusion for stationary integral varifolds. The primary difficulty for this lies in understanding branch points, namely non-immersed singular points where one tangent cone is a plane with multiplicity at least 2. Both the uniqueness of such tangent cones and the optimal dimension bound are not known (the latter is known for area minimising currents, having been settled by the monumental work of Almgren).

In this talk, I will discuss recent work with Spencer Becker-Kahn and Neshan Wickramasekera concerning these questions, in which we show that a simple topological structural condition on the varifold in “flat density gaps” is sufficient to prove that the local structure about density 2 branch points is given by a 2-valued function (with a regularity estimate). This is a consequence of a more general epsilon-regularity theorem, akin to Allard’s regularity theorem except in a multiplicity 2 setting.

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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