Almgren minimals sets, minimal cones, unions and products

Abstract: The notion of Almgren minimal sets is a way to try to solve Plateau’s problem in the setting of sets. To study local structures for these sets, one does blow-ups at each point, and the blow-up limits turn out to be minimal cones. People then would like to know the list of all minimal cones.

The list of 1 or 2-dimensional minimal cones in $\mathbb R^3$ are known for over a century. For other dimensions and codimensions, much less is known. Up to now there is no general way to classify all possible minimal cones. One typical way is to test unions and products of known minimal cones.

In this talk, we will first introduce basic notions and facts on Almgren minimal sets and minimal cones. Then we will discuss the minimality of unions and products of two minimal cones.

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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