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January 2019 Vanishing Pohozaev constant and removability of singularities
Jürgen Jost, Chunqin Zhou, Miaomiao Zhu
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J. Differential Geom. 111(1): 91-144 (January 2019). DOI: 10.4310/jdg/1547607688


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 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.


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Jürgen Jost. Chunqin Zhou. Miaomiao Zhu. "Vanishing Pohozaev constant and removability of singularities." J. Differential Geom. 111 (1) 91 - 144, January 2019.


Received: 14 November 2015; Published: January 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07004532
MathSciNet: MR3909905
Digital Object Identifier: 10.4310/jdg/1547607688

Primary: 35A20 , 35B44 , 35J60

Keywords: Blow-up , conical singularity , Pohozaev constant , Pohozaev identity , Super-Liouville equation

Rights: Copyright © 2019 Lehigh University


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Vol.111 • No. 1 • January 2019
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