Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Ricci flatness of asymptotically locally Euclidean metrics


Authors: Lei Ni, Yuguang Shi and Luen-Fai Tam
Journal: Trans. Amer. Math. Soc. 355 (2003), 1933-1959
MSC (2000): Primary 32Q15
DOI: https://doi.org/10.1090/S0002-9947-02-03242-7
Published electronically: December 18, 2002
MathSciNet review: 1953533
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this article we study the metric property and the function theory of asymptotically locally Euclidean (ALE) Kähler manifolds. In particular, we prove the Ricci flatness under the assumption that the Ricci curvature of such manifolds is either nonnegative or nonpositive. The result provides a generalization of previous gap type theorems established by Greene and Wu, Mok, Siu and Yau, etc. It can also be thought of as a general positive mass type result. The method also proves the Liouville properties of plurisubharmonic functions on such manifolds. We also give a characterization of Ricci flatness of an ALE Kähler manifold with nonnegative Ricci curvature in terms of the structure of its cone at infinity.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32Q15

Retrieve articles in all journals with MSC (2000): 32Q15


Additional Information

Lei Ni
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
Email: lni@math.ucsd.edu

Yuguang Shi
Affiliation: Department of Mathematics, Peking University, Beijing, 100871, China
Email: ygshi@math.pku.edu.cn

Luen-Fai Tam
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Email: lftam@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/S0002-9947-02-03242-7
Received by editor(s): July 25, 2002
Published electronically: December 18, 2002
Additional Notes: The research of the first author was partially supported by NSF grant DMS-0196405 and DMS-0203023, USA
The research of the second author was partially supported by NSF of China, project 10001001
The research of the third author was partially supported by Earmarked Grant of Hong Kong #CUHK4217/99P
Article copyright: © Copyright 2002 American Mathematical Society