MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

The Boundary Value Problem for the Super-Liouville Equation

Jürgen Jost, Guofang Wang, Chunqin Zhou and Miaomiao Zhu


We study the boundary value problem for the -- conformally invariant -- super Liouville functional \begin{equation*} E\left( u,\psi \right) =\int_{M}\{\frac 12 \left| \nabla u\right| ^2+K_gu+\left\langle (D+e^u)\psi ,\psi \right\rangle -e^{2u}\}dz \end{equation*}} that couples a function $u$ and a spinor $\psi$ 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 $\psi$. 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.


Related publications

2014 Repository Open Access
Jürgen Jost, Guofang Wang, Chunqin Zhou and Miaomiao Zhu

The boundary value problem for the Super-Liouville equation

In: Annales de l'Institut Henri Poincaré / C, 31 (2014) 4, pp. 685-706