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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the linear stability of Kähler-Ricci solitons


Authors: Stuart J. Hall and Thomas Murphy
Journal: Proc. Amer. Math. Soc. 139 (2011), 3327-3337
MSC (2010): Primary 53C44; Secondary 53C25
Published electronically: March 9, 2011
MathSciNet review: 2811287
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Abstract: We show that Kähler-Ricci solitons with $ \dim H^{(1,1)}(M)\ge 2$ are linearly unstable. This extends the results of Cao-Hamilton-Ilmanen in the Kähler-Einstein case.


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

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Additional Information

Stuart J. Hall
Affiliation: Department of Mathematics, Imperial College, London, SW7 2AZ, United Kingdom
Email: stuart.hall06@imperial.ac.uk

Thomas Murphy
Affiliation: School of Mathematical Sciences, University College Cork, Ireland
Email: tommy.murphy@ucc.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10948-1
PII: S 0002-9939(2011)10948-1
Keywords: Ricci solitons, Perelman’s $\nu$-functional, linear stability
Received by editor(s): August 21, 2010
Published electronically: March 9, 2011
Additional Notes: This work forms part of the first author’s Ph.D thesis funded by the EPSRC. He would like to thank his advisor, Professor Simon Donaldson, for his comments and encouragement during the course of this work.
The second author was supported by an IRCSET postgraduate fellowship. The authors would also like to thank Professor Huai-Dong Cao for useful communications.
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.