Showing papers by "Miaomiao Zhu published in 2016"

Regularity at the free boundary for Dirac-harmonic maps from surfaces

Abstract: We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our methods also lead to the full interior \(\epsilon \)-regularity and smooth estimates for weakly Dirac-harmonic maps in all dimensions.

Quantization for a nonlinear Dirac equation

Abstract: We study solutions of certain nonlinear Dirac-type equations on Riemann spin surfaces. We first improve an energy identity theorem for a sequence of such solutions with uniformly bounded energy in the case of a fixed domain. Then, we prove the corresponding energy identity in the case that the equations have constant coefficients and the domains possibly degenerate to a spin surface with only Neveu-Schwarz type nodes.

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Abstract: 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 Riviere's regularity theory and Riesz potential theory.