Abstract
AbstractThis article studies hypoellipticity on general filtered manifolds. We extend the Rockland criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and describe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Reference81 articles.
1. Atiyah, M.F., Singer, I.M.: The index of elliptic operators. I. Ann. of Math. 2(87), 484–530 (1968)
2. Baum, P.F., van Erp, E.: $$K$$-homology and index theory on contact manifolds. Acta Math. 213(1), 1–48 (2014)
3. Beals, R., Greiner, P.: Calculus on Heisenberg manifolds. In: Annals of Mathematics Studies, vol. 119, Princeton University Press, Princeton (1988)
4. Biquard, O.: Métriques d’Einstein asymptotiquement symétriques. Astérisque 265, vi+109 (2000)
5. Bryant, R.L.: Conformal geometry and 3-plane fields on 6-manifolds. In: Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, vol. 1502, Kyoto University, pp. 1–15(2006). Preprint available at arXiv:math/0511110
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献