Energy quantization for a singular super-Liouville boundary value problem
Jürgen Jost, Chunqin Zhou, and Miaomiao Zhu
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Submission date: 27. Aug. 2019
MSC-Numbers: 35J60, 35A20, 35B44
Keywords and phrases: Super-Liouville equation, Pohozaev constant, conical singularity, blow-up, energy identity, Boundary value problem, chiral boundary condition
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In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis, the blow-up analysis usually strongly utilizes conformal invariance, which yields a Noether current from which strong estimates can be derived. Here, however, the conical singularities destroy conformal invariance. Therefore, we develop another, more general, method that uses the vanishing of the Pohozaev constant for such solutions to deduce the removability of boundary singularities.