Proceedings of the American Mathematical Society

Author(s): Gilles Carron
Journal: Proc. Amer. Math. Soc. 135 (2007), 1579-1583.
MSC (2000): Primary 58A14; Secondary 58J10
Posted: January 9, 2007
Retrieve article in: PDF

Abstract: We give a counterexample to the following conjecture of E. Bueler: ``The de Rham cohomology of any complete Riemannian manifold is isomorphic to a weighted

cohomology where the weight is the heat kernel."

1.: Z.M. Ahmed and D.W. Stroock, A Hodge theory for some non-compact manifolds, J. Differential Geom., 54, (2000), ${\rm n}^o$ 1, 177-225. MR 1815415 (2002j:58033)
2.: E. Bueler, The heat kernel weighted Hodge Laplacian on non compact manifolds, Trans. A.M.S. 351, 2 (1999), 683-713. MR 1443866 (99d:58164)
3.: S. Gallot, D. Meyer. Opérateur de courbure et laplacien des formes différentielles d'une variété Riemannienne. J. Math. Pures Appli., 54 (1975), 259-284. MR 0454884 (56:13128)
4.: F.-Z. Gong, and F.Y. Wang, Heat kernel estimates with application to compactness of manifolds, Q. J. Math., 52, (2001), ${\rm n}^o$ 2, 171-180. MR 1838361 (2002c:58039)
5.: L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds. J. Diff. Geometry, 36, (1992), 417-450. MR 1180389 (93m:58122)
6.: N. Yeganefar, Sur la $L\sp 2$ -cohomologie des variétés à courbure négative, Duke Math. J., 122, (2004), ${\rm n}^o$ 1, 145-180. MR 2046810 (2005b:58026)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58A14, 58J10

Gilles Carron
Affiliation: Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, 2, rue de la Houssinière, B.P.~92208, 44322 Nantes Cedex~3, France
Email: Gilles.Carron@math.univ-nantes.fr

DOI: 10.1090/S0002-9939-07-08713-8
PII: S 0002-9939(07)08713-8
Keywords: $L^2$ cohomology
Received by editor(s): January 19, 2006
Received by editor(s) in revised form: February 24, 2006
Posted: January 9, 2007
Communicated by: Mikhail Shubin
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS