The purpose of this paper is to set up a formalism inspired by non-Archimedean geometry to
study K-stability. We first provide a detailed analysis of Duistermaat–Heckman measures in …

It is shown that any, possibly singular, Fano variety X admitting a Kähler-Einstein metric is K-
polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the …

For any flat projective family (𝒳, ℒ)→ C such that the generic fibre 𝒳η is a klt ℚ-Fano variety
and L|_X_η∼_Q-K_X_η, we use the techniques from the minimal model program (MMP) to …

Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a
positive metric on a test configuration for (X, L). For many common functionals in Kähler …

Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of
quantities associated to valuations, which has been essential to all recent progress in the …

We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a
notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admitting …

arXiv:2110.10386v1 [math.DG] 20 Oct 2021 Page 1 arXiv:2110.10386v1 [math.DG] 20 Oct
2021 A UNIFORM VERSION OF THE YAU-TIAN-DONALDSON CORRESPONDENCE FOR …

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This article is concerned with an observation for proving non-existence of canonical Kahler
metrics. The idea is to use a rather explicit type of degeneration that applies in many …

In this thesis, we study several problems related to the existence problem of Kahler-Einstein
metric on Fano manifold. After introduction in the first chapter, in the second chapter, we …