Concentration phenomena for the fractional Q-curvature equation in dimension 3 and fractional Poisson formulas
Entity
UAM. Departamento de MatemáticasPublisher
WileyDate
2021-01-21Citation
10.1112/jlms.12437
Journal of the London Mathematical Society 104.1 (2021): 423-451
ISSN
0024-6107 (print); 1469-7750 (online)DOI
10.1112/jlms.12437Editor's Version
https://doi.org/10.1112/jlms.12437Subjects
35J30; 35J91; 35S05; 53A55 (primary); MatemáticasRights
®2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licenceAbstract
We study the compactness properties of metrics of prescribed fractional (Formula presented.) -curvature of order 3 in (Formula presented.). We will use an approach inspired from conformal geometry, seeing a metric on a subset of (Formula presented.) as the restriction of a metric on (Formula presented.) with vanishing fourth-order (Formula presented.) -curvature. We will show that a sequence of such metrics with uniformly bounded fractional (Formula presented.) -curvature can blow up on a large set (roughly, the zero set of the trace of a non-positive bi-harmonic function (Formula presented.) in (Formula presented.)), in analogy with a four-dimensional result of Adimurthi–Robert–Struwe, and construct examples of such behaviour. In doing so, we produce general Poisson-type representation formulas (also for higher dimension), which are of independent interest
Files in this item
Google Scholar:DelaTorre, Azahara
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González, María del Mar
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Hyder, Ali
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Martinazzi, Luca
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