We prove that on any log Fano pair of dimension n whose stability threshold is less than
n+1n, any valuation computing the stability threshold has a finitely generated associated …

The study of complex Monge–Ampere equations on compact Kähler manifolds is an
important part of the interface between complex analysis and differential geometry …

Kâ•’Stability and Kählerâ•’Einstein Metrics Page 1 K-Stability and Kähler-Einstein Metrics
GANG TIAN Beijing University Princeton University Abstract We prove that if a Fano manifold …

We give a variational proof of a version of the Yau–Tian–Donaldson conjecture for twisted
Kähler–Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in …

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 …

Let X be a normal complex projective variety with at worst klt singularities, and L a big line
bundle on X. We use valuations to study the log canonical threshold of L, as well as another …

A valuative criterion for uniform K-stability of ℚ-Fano varieties Skip to content Should you
have institutional access? Here's how to get it ... De Gruyter € EUR - Euro £ GBP - Pound …

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 …

In this paper, we prove the openness of K-semistability in families of log Fano pairs by
showing that the stability threshold is a constructible function on the fibers. We also prove …

We prove the existence and uniqueness of Kähler–Einstein metrics on ℚ-Fano varieties with
log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional …