Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinity
| dc.creator | Aubry, Erwann | |
| dc.creator | Guillarmou, Colin | |
| dc.date | 2008-08-05 | |
| dc.date.accessioned | 2026-07-07T09:54:42Z | |
| dc.date.available | 2026-07-07T09:54:42Z | |
| dc.description | For odd dimensional Poincaré-Einstein manifolds $(X^{n+1},g)$, we study the set of harmonic $k$-forms (for $k<\ndemi$) which are $C^m$ (with $m\in\nn$) on the conformal compactification $\bar{X}$ of $X$. This is infinite dimensional for small $m$ but it becomes finite dimensional if $m$ is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology $H^k(\bar{X},\pl\bar{X})$ and the kernel of the Branson-Gover \cite{BG} differential operators $(L_k,G_k)$ on the conformal infinity $(\pl\bar{X},[h_0])$. In a second time we relate the set of $C^{n-2k+1}(Λ^k(\bar{X}))$ forms in the kernel of $d+δ_g$ to the conformal harmonics on the boundary in the sense of \cite{BG}, providing some sort of long exact sequence adapted to this setting. This study also provides another construction of Branson-Gover differential operators, including a parallel construction of the generalization of $Q$ curvature for forms. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/0808.0552 | |
| dc.identifier | http://arxiv.org/abs/0808.0552 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166415 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A30, 58J32 | |
| dc.title | Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinity | |
| dc.type | text |