Concentration phenomena for the fractional Q-curvature equation in dimension 3 and fractional Poisson formulas
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 present...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad Autónoma de Madrid |
| Repository: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Language: | English |
| OAI Identifier: | oai:repositorio.uam.es:10486/705428 |
| Online Access: | http://hdl.handle.net/10486/705428 https://dx.doi.org/10.1112/jlms.12437 |
| Access Level: | Open access |
| Keyword: | 35J30 35J91 35S05 53A55 (primary) Matemáticas |
| Summary: | 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 |
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