Event Details
Título: Concentration phenomena for the fractional \(Q\)-curvature equation in dimension 3 and fractional Poisson formulas.
Impartida por: Azahara De la Torre.
Abstract: We study compactness properties of metrics of prescribed fractional \(Q\)-curvature of order \(3\) in \(\mathbb{R}^3\). We use an approach inspired from conformal geometry, regarding a metric on a subset of \(\mathbb{R}^3\) as the restriction of a metric on \(\mathbb{R}^4_+\) with vanishing fourth-order \(Q\)-curvature. In particular, in analogy with a \(4\)-dimensional result of Adimurthi, Robert and Struwe, we prove that a sequence of such metrics with uniformly bounded fractional \(Q\)-curvature can blow up on a large set (roughly, the zero set of the trace of a nonpositive biharmonic function \(\Phi\) in \(\mathbb{R}^4_+\)), and we also construct examples of such behaviour. Towards this result, an intermediate step of independent interest is the construction of general Poisson-type representation formulas (also for higher dimension).
This is a work done in collaboration with María del Mar González, Ali Hyder and Luca Martinazzi.
5 de septiembre de 2019, 10:00, Seminario 1ª planta IEMath-GR
Impartida por: Azahara De la Torre.
Abstract: We study compactness properties of metrics of prescribed fractional \(Q\)-curvature of order \(3\) in \(\mathbb{R}^3\). We use an approach inspired from conformal geometry, regarding a metric on a subset of \(\mathbb{R}^3\) as the restriction of a metric on \(\mathbb{R}^4_+\) with vanishing fourth-order \(Q\)-curvature. In particular, in analogy with a \(4\)-dimensional result of Adimurthi, Robert and Struwe, we prove that a sequence of such metrics with uniformly bounded fractional \(Q\)-curvature can blow up on a large set (roughly, the zero set of the trace of a nonpositive biharmonic function \(\Phi\) in \(\mathbb{R}^4_+\)), and we also construct examples of such behaviour. Towards this result, an intermediate step of independent interest is the construction of general Poisson-type representation formulas (also for higher dimension).
This is a work done in collaboration with María del Mar González, Ali Hyder and Luca Martinazzi.
5 de septiembre de 2019, 10:00, Seminario 1ª planta IEMath-GR
