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MiS Preprint

Vanishing Pohozaev constant and removability of singularities

Jürgen Jost, Chunqin Zhou and Miaomiao Zhu


Conformal invariance of two-dimensional variational problems is a condition known to enable a blow-up analysis of solutions and to deduce the removability of singularities. In this paper, we identify another condition that is not only sufficient, but also necessary for such a removability of singularities. This is the validity of the Pohozaev identity. In situations where such an identity fails to hold, we introduce a new quantity, called the {\it Pohozaev constant}, which on one hand measures the extent to which the Pohozaev identity fails and on the other hand provides a characterization of the singular behavior of a solution at an isolated singularity. We apply this to the blow-up analysis for super-Liouville type equations on Riemann surfaces with conical singularities, because in the presence of such singularities, conformal invariance no longer holds and a local singularity is in general non-removable unless the Pohozaev constant is vanishing.

Nov 19, 2015
Nov 20, 2015

Related publications

2019 Repository Open Access
Jürgen Jost, Chunqin Zhou and Miaomiao Zhu

Vanishing Pohozaev constant and removability of singularities

In: Journal of differential geometry, 111 (2019) 1, pp. 91-144