Abstract
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.
Highlights
Many problems with a noncompact symmetry group, like the conformal group, are limit cases where the Palais–Smale condition no longer applies, and solutions may blow up at isolated singularities, see for instance [31]
Germany associated Noether current whose algebraic structure can be turned into estimates
For harmonic map type problems, finiteness of the energy functional in question implies that that differential is in L1
Summary
Many problems with a noncompact symmetry group, like the conformal group, are limit cases where the Palais–Smale condition no longer applies, and solutions may blow up at isolated singularities, see for instance [31]. We shall apply this strategy to the blow-up analysis of the (super-) Liouville boundary problem on surfaces with conical singularities. To this purpose, let M be a compact Riemann surface with nonempty boundary ∂ M and with a spin structure. Is a geodesic ball of (M, g) at p For this purpose, we need to study the following local super-Liouville boundary value problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
