Journal of the Mathematical Society of Japan

Relative stability and extremal metrics


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In this paper, by clarifying the concept of relative K-stability in [28], we shall solve the stability part of an extremal Kähler version of Donaldson-Tian-Yau's Conjecture. This extends the results in [15] and [27]. We then propose a program to solve the existence part of the conjecture.

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J. Math. Soc. Japan, Volume 66, Number 2 (2014), 535-563.

First available in Project Euclid: 23 April 2014

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Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32Q15: Kähler manifolds 32Q26: Notions of stability

K-stability extremal Kähler metrics relative stability test configurations Donaldson-Tian-Yau's Conjecture


MABUCHI, Toshiki. Relative stability and extremal metrics. J. Math. Soc. Japan 66 (2014), no. 2, 535--563. doi:10.2969/jmsj/06620535.

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