Skip Navigation


International Mathematics Research Notices Advance Access originally published online on February 28, 2009
International Mathematics Research Notices (2009) 2009:2347-2373, doi:10.1093/imrn/rnp019 published on June 28, 2009
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
2009/13/2347    most recent
rnp019v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Juillet, N.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group

Nicolas Juillet

Institut Fourier BP 74, UMR 5582, Université Grenoble I, 38402 Saint-Martin-d'Hères Cedex, France, and Institute for Applied Mathematics, University of Bonn, Poppelsdorfer Allee 82, 53 115 Bonn, Germany

Correspondence: Correspondence to be sent to: nicolas.juillet{at}ujf-grenoble.fr

We prove that no curvature-dimension bound CD(K,N) holds in any Heisenberg group Formula . On the contrary, the measure contraction property MCP(0, 2n + 3) holds and is optimal for the dimension 2n + 3. For the nonexistence of a curvature-dimension bound, we prove that the generalized "geodesic" Brunn–Minkowski inequality is false in Formula . We also show in a new and direct way (and for all Formula ), that the general "multiplicative" Brunn–Minkowski inequality with dimension N > 2n + 1 is false.

Communicated by Prof. John Lott


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.