Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu, Miaomiao Zhu
Published 2016-10-07Version 1
We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler--Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivi\`ere's regularity theory and Riesz potential theory.
$n$-harmonic coordinates and the regularity of conformal mappings
Regularity of minimal surfaces near quadratic cones
$C^{1,α}$-regularity for surfaces with $H$ in $L^p$
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