Geodesic
Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 911-957 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

For odd dimensional Poincaré–Einstein manifolds (Xn+​1,g), we study the set of harmonic k-forms (for k/2) which are Cm (with m∈N) on the conformal compactification Xˉ 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 Hk(Xˉ,∂Xˉ) and the kernel of the Branson–Gover [3] differential operators (Lk​,Gk​) on the conformal ifinity (∂Xˉ,[h0​]). In a second time we relate the set of Cn−2k+1(Λk(Xˉ)) forms in the kernel of d+δg​ to the conformal harmonics on the boundary in the sense of [3], 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.
DOI : 10.4171/jems/271
Classification : 53-XX, 58-XX, 00-XX
Keywords: Conformal harmonic forms, Branson–Gover operator, harmonic forms 
@article{JEMS_2011_13_4_a3,
     author = {Erwann Aubry and Colin Guillarmou},
     title = {Conformal harmonic forms, {Branson{\textendash}Gover} operators and {Dirichlet} problem at infinity},
     journal = {Journal of the European Mathematical Society},
     pages = {911--957},
     year = {2011},
     volume = {13},
     number = {4},
     doi = {10.4171/jems/271},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/271/}
}
TY  - JOUR
AU  - Erwann Aubry
AU  - Colin Guillarmou
TI  - Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
JO  - Journal of the European Mathematical Society
PY  - 2011
SP  - 911
EP  - 957
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/271/
DO  - 10.4171/jems/271
ID  - JEMS_2011_13_4_a3
ER  - 
%0 Journal Article
%A Erwann Aubry
%A Colin Guillarmou
%T Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
%J Journal of the European Mathematical Society
%D 2011
%P 911-957
%V 13
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/271/
%R 10.4171/jems/271
%F JEMS_2011_13_4_a3
Erwann Aubry; Colin Guillarmou. Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity. Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 911-957. doi: 10.4171/jems/271

Cité par Sources :