Duke Mathematical Journal

Extremal metrics on blowups

Claudio Arezzo, Frank Pacard, and Michael Singer

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In this paper we provide conditions that are sufficient to guarantee the existence of extremal metrics on blowups at finitely many points of Kähler manifolds which already carry an extremal metric. As a particular case, we construct extremal metrics on P2 blown-up k points in general position, with k<m+2.

Article information

Duke Math. J., Volume 157, Number 1 (2011), 1-51.

First available in Project Euclid: 16 March 2011

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Zentralblatt MATH identifier

Primary: 32J27: Compact Kähler manifolds: generalizations, classification
Secondary: 32Q15: Kähler manifolds 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]


Arezzo, Claudio; Pacard, Frank; Singer, Michael. Extremal metrics on blowups. Duke Math. J. 157 (2011), no. 1, 1--51. doi:10.1215/00127094-2011-001. https://projecteuclid.org/euclid.dmj/1300281532

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