Skip Navigation

International Mathematics Research Notices (2000) 2000:607-623, doi:10.1155/S1073792800000337
This Article
Right arrow Full Text (PDF)
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 Chen, X.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

On the lower bound of the Mabuchi energy and its application

Xiuxiong Chen

In this article, we introduce some new functional which is convex along geodesic in the infinite dimensional space of Kähler metrics/potentials in a fixed Kähler class. This functional is also introduced by S. Donaldson in a slightly wider context. The Euler-Lagrange equation of this functional is some new Monge Ampere type equation. When C1 < 0, we can construct such a convex functional which is dominated by the Mabuchi energy. Thus we provide a new approach in bounding the Mabuchi energy, namely bounding this new functional from below. Thus it is crucial to find a critical point of this new functional. In complex surface, we prove a necessary and sufficent condition for this new functional to have a critical point.


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.