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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) 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.
Energy quantization for a singular super-Liouville boundary value problem
Jürgen Jost, Chunqin Zhou and Miaomiao ZhuAbstract
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.
- Received:
- 27.08.19
- Published:
- 27.08.19
- MSC Codes:
- 35J60, 35A20, 35B44
- Keywords:
- Super-Liouville equation, Pohozaev constant, conical singularity, blow-up, energy identity, Boundary value problem, chiral boundary condition