On the regularity of area minimzing currents mod(p)

Abstract: joint work with C. De Lellis, A Marches and S. Stuvard

In this talk I would like to give a glimpse on the regularity of area minimzing currents mod(p).

Motivation: If one considers real soap films one notice that from time to time one can find configurations where different soap films join on a common piece. One possibility to allow this kind of phenomenon is to consider flat chains with coefficients in $\mathbb Z_p$. For instance for $p = 2$ one can deal with unoriented surfaces, for $p = 3$ one allows triple junctions.

Considering area minimzing currents within this class the aim is to give a bound on the Hausdorff dimension of the singular set sing(T) in the interior. These are alle points where the precise representative of the minimiser T is not even locally supported on a piece of a $C^{1,\alpha}$ regular surface.
After a short introduction into general theory of currents mod(p), I will give you glimpse on the previously known results and on our new bound on the Hausdorff dimension of the set. If time permits I will give a short outlook of what we would be the expected result.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

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Online Seminar "Geometric Analysis"

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