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Convergence of general inverse $ \sigma_k$-flow on Kähler manifolds with Calabi ansatz


Authors: Hao Fang and Mijia Lai
Journal: Trans. Amer. Math. Soc. 365 (2013), 6543-6567
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/S0002-9947-2013-05947-8
Published electronically: August 19, 2013
MathSciNet review: 3105762
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Abstract: We study the convergence behavior of the general inverse $ \sigma _k$-flow on Kähler manifolds with initial metrics satisfying the Calabi ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negatively self-intersected subvarieties are formed as a result of partial blow up.


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Additional Information

Hao Fang
Affiliation: Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, Iowa 52242
Email: hao-fang@uiowa.edu

Mijia Lai
Affiliation: Department of Mathematics, University of Rochester, 915 Hylan Building, RC Box 270138, Rochester, New York 14627
Email: lai@math.rochester.edu

DOI: https://doi.org/10.1090/S0002-9947-2013-05947-8
Received by editor(s): March 23, 2012
Received by editor(s) in revised form: June 13, 2012
Published electronically: August 19, 2013
Additional Notes: The first author was partially supported by NSF grant DMS1008249.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.