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

<center class="math-display"> <img src="/fileadmin/preprint_img/2011/tex_1686a0x.png" alt=" &amp;#x222B; E (u,&amp;#x03C8; ) = {1|&amp;#x2207;u |2 + K u+ &amp;#x27E8;(D/ + eu)&amp;#x03C8;,&amp;#x03C8; &amp;#x27E9;- e2u}dz M 2 g " class="math-display"></center>

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.

18.10.2019, 02:14