Abelian actions with globally hypoelliptic leafwise Laplacian and rigidity
2016 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 129, no 1, 139-163 p.Article in journal (Refereed) Published
In this paper, we prove several results concerning smooth Rk actions on a smooth compact manifold with the property that their leafwise Laplacian is globally hypoelliptic. Such actions are necessarily uniquely ergodic and minimal, and their cohomology is often finite dimensional, even trivial. Further, we consider a class of examples of R2 actions on two-step nilmanifolds that have globally hypoelliptic leafwise Laplacian, and we show transversal local rigidity under certain Diophantine conditions.
Place, publisher, year, edition, pages
Springer-Verlag New York, 2016. Vol. 129, no 1, 139-163 p.
IdentifiersURN: urn:nbn:se:kth:diva-197191DOI: 10.1007/s11854-016-0018-8ScopusID: 2-s2.0-84983607426OAI: oai:DiVA.org:kth-197191DiVA: diva2:1055478
QC 201612122016-12-122016-11-302016-12-12Bibliographically approved