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Harmonic forms on manifolds with edges

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posted on 31.03.2015, 10:15 by Eugenie HunsickerEugenie Hunsicker, Rafe Mazzeo
Let (X, g) be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various polynomially weighted de Rham cohomology spaces of X, as well as the associated spaces of harmonic forms. In the unweighted case, this is closely related to recent work of Cheeger and Dai [5]. Because the metric g is incomplete, this requires a consideration of the various choices of ideal boundary conditions at the singular set. We also calculate the space of L2 harmonic forms for any complete edge metric on the regular part of X.

Funding

The first author was partially supported by the NSF through an ROA supplement to Grant DMS- 0204730. The second author was supported by the NSF through Grant DMS-0204730.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

Volume

52

Pages

3229 - 3272

Citation

HUNSICKER, E. and MAZZEO, R., 2005. Harmonic forms on manifolds with edges. International Mathematics Research Notices, 52, pp. 3229 - 3272

Publisher

Oxford University Press / © Hindawi Publishing Corporation

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2005

Notes

This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record HUNSICKER, E. and MAZZEO, R., 2005. Harmonic forms on manifolds with edges. International Mathematics Research Notices, 52, pp. 3229 - 3272 is available online at: http://dx.doi.org/10.1155/IMRN.2005.3229

ISSN

1687-0247

Language

en

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