The boundary value problem for the super-Liouville equation
Jürgen Jost
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, GermanyGuofang Wang
Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, GermanyChunqin Zhou
Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, ChinaMiaomiao Zhu
Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK
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Abstract
We study the boundary value problem for the — conformally invariant — super-Liouville functional
that couples a function and a spinor on a Riemann surface. The boundary condition that we identify (motivated by quantum field theory) couples a Neumann condition for with a chirality condition for . Associated to any solution of the super-Liouville system is a holomorphic quadratic differential , and when our boundary condition is satisfied, becomes real on the boundary. We provide a complete regularity and blow-up analysis for solutions of this boundary value problem.
Cite this article
Jürgen Jost, Guofang Wang, Chunqin Zhou, Miaomiao Zhu, The boundary value problem for the super-Liouville equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 4, pp. 685–706
DOI 10.1016/J.ANIHPC.2013.06.002