Preprint 60/2011

The Boundary Value Problem for the Super-Liouville Equation

Jürgen Jost, Guofang Wang, Chunqin Zhou,and Miaomiao Zhu

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Submission date: 08. Sep. 2011 (revised version: July 2013)
Pages: 24
published in: Annales de l'Institut Henri Poincaré / C, 31 (2014) 4, p. 685-706 
DOI number (of the published article): 10.1016/j.anihpc.2013.06.002
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>We study the boundary value problem for the – conformally invariant – super Liouville functional

         ∫ E (u,ψ ) =   {1|∇u |2 + K u+ ⟨(D/ + eu)ψ,ψ ⟩- e2u}dz           M  2         g

that couples a function u and a spinor ψ on a Riemann surface. The boundary condition that we identify (motivated by quantum field theory) couples a Neumann condition for u with a chirality condition for ψ. Associated to any solution of the super Liouville system is a holomorphic quadratic differential T(z), and when our boundary condition is satisfied, T becomes real on the boundary.
We provide a complete regularity and blow-up analysis for solutions of this boundary value problem.

07.10.2017, 01:42