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Suppose that a polarised Kähler manifold (X, L) admits an extremal metric ω ω. We prove
that there exists a sequence of Kähler metrics {ω _k\} _k ω kk, converging to ω ω as k → ∞ …

We show that a Kähler-Ricci soliton on a Fano manifold can always be smoothly
approximated by a sequence of relative anticanonically balanced metrics, also called …

We study algebro-geometric consequences of the quantised extremal Kähler metrics,
introduced in the previous work of the author. We prove that the existence of quantised …

In the first part of this paper we outline the constructions and properties of Fedosov star
product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and …

The first three sections of this paper are a survey of the author's work on balanced metrics
and stability notions in algebraic geometry. The last section is devoted to proving the well …

For a polarized Kähler manifold $(X, L) $, we show the equivalence between relative
balanced embeddings introduced by Mabuchi and $\sigma $-balanced embeddings …

For a polarized K\" ahler manifold $(X, L) $, we show the equivalence between relative
balanced embeddings introduced by Mabuchi and $\sigma $-balanced embeddings …

The first three sections of this paper are a survey of the author's work on balanced metrics
and stability notions in algebraic geometry. The last section is devoted to proving the well …

Ce texte de synthèse présente des travaux en géométrie hermitienne, à l'interface de la
géométrie algébrique complexe, de l'analyse géométrique et de la physique mathématique …