, Volume 15, Issue 3, pp 697-719
Date: 16 Aug 2005

Kähler–Ricci solitons on compact complex manifolds with C 1(M) > 0

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In this paper, we discuss the relation between the existence of Kähler–Ricci solitons and a certain functional associated to some complex Monge–Ampère equation on compact complex manifolds with positive first Chern class. In particular, we obtain a strong inequality of Moser–Trudinger type on a compact complex manifold admitting a Kähler–Ricci soliton.

Received: October 2004 Revised: February 2005 Accepted: February 2005