The boundary value problem for the super-Liouville equation

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

doi:10.1016/j.anihpc.2013.06.002

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

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 4, pp. 685-706.

Résumé

We study the boundary value problem for the — conformally invariant — super-Liouville functional

E (u, ψ) = \int_{M} {\frac{1}{2} {| \nabla u |}^{2} + K_{g} u + 〈 (D ̸ + e^{u}) ψ, ψ 〉 - e^{2 u}} d z

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.

MR Zbl

DOI : 10.1016/j.anihpc.2013.06.002

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     author = {Jost, J\"urgen and Wang, Guofang and Zhou, Chunqin and Zhu, Miaomiao},
     title = {The boundary value problem for the {super-Liouville} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {685--706},
     publisher = {Elsevier},
     volume = {31},
     number = {4},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.06.002},
     mrnumber = {3249809},
     zbl = {1319.30028},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.06.002/}
}

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Jost, Jürgen; Wang, Guofang; Zhou, Chunqin; Zhu, Miaomiao. The boundary value problem for the super-Liouville equation. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 4, pp. 685-706. doi : 10.1016/j.anihpc.2013.06.002. http://www.numdam.org/articles/10.1016/j.anihpc.2013.06.002/

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