4 papers
Compactification of metric moduli space of surfaces
Zexuan Ouyang, Gang Tian
We prove a conjecture of Odaka--Oshima, which says that there is an algebraic description of the Gromov--Hausdorff compactification of all unit-diameter hyperkähler metrics on K3…
Hermitian-Einstein Metrics on Parabolic Bundles over compact complex surfaces
Xilun Li, Gang Tian
We prove the Kobayashi-Hitchin correspondence for parabolic bundles over compact nonKähler surfaces with simple normal crossing divisor or compact nonKähler manifolds of any dime…
Stability thresholds for big classes
Chenzi Jin, Yanir A. Rubinstein, Gang Tian
In 1987, the -invariant theorem gave a fundamental criterion for existence of Kahler-Einstein metrics on smooth Fano manifolds. In 2012, Odaka-Sano extended the framework to $\…
Asymptotics of discrete Okounkov bodies and thresholds
Chenzi Jin, Yanir A. Rubinstein, Gang Tian
This article initiates the study of discrete Okounkov bodies and higher-dimensional Weierstrass gap phenomena, with applications to asymptotic analysis of stability and global log…