Jonas Hirsch - On the regularity of area minimzing currents mod(p)

Tuesday, October 6, 2020 - 13:00
Speaker Information
Jonas Hirsch
University of Leipzig

Abstract or Additional Information

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 Zp\mathbb Z_pZp​. For instance for p=2p = 2p=2 one can deal with unoriented surfaces, for p=3p = 3p=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 C1,αC^{1,\alpha}C1,α 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.

Research Area