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
