## Duke Mathematical Journal

### Extremal metrics on blowups

#### Abstract

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 $\mathbb {P}^2$ blown-up k points in general position, with $k \lt m+2$.

#### Article information

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

Dates
First available in Project Euclid: 16 March 2011

https://projecteuclid.org/euclid.dmj/1300281532

Digital Object Identifier
doi:10.1215/00127094-2011-001

Mathematical Reviews number (MathSciNet)
MR2783927

Zentralblatt MATH identifier
1221.32008

#### Citation

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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