8 citations · 25 across the 13 of their papers we have counts for
13 papers · 1 filter
Optimal geometric estimates for compact Kähler manifolds of a Nash entropy bound
Weiqi Zhang, Yashan Zhang
We prove Sobolev-type inequality and local volume noncollapsing with optimal exponents for compact Kähler manifolds of uniformly bounded -Nash entropy.
Positivity in Foliated Manifolds and Geometric Applications
Yashan Zhang, Tao Zheng
We introduce the notion of positivity for a real basic class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity…
A note on Teissier problem for nef classes
Yashan Zhang
Teissier problem aims to characterize the equality case of Khovanskii-Teissier type inequality for -classes on a compact Kähler manifold. When each of the involved -c…
On almost quasi-negative holomorphic sectional curvature
Yashan Zhang, Tao Zheng
A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact Kähler manifold admitting a Kähler metric of quasi-negative holomorphic sectional curvature has an a…
On higher-rank Khovanskii-Teissier inequalities
Yashan Zhang
We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain…
Local curvature estimates of long-time solutions to the Kähler-Ricci flow
Frederick Tsz-Ho Fong, Yashan Zhang
We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundles. Using these es…
Infinite-time singularity type of the Kähler-Ricci flow II
Yashan Zhang
On a compact Kähler manifold with semi-ample canonical line bundle and Kodaira dimension one, we observe a relation between the infinite-time singularity type of the Kähler-Ricci f…
On a twisted conical Kähler-Ricci flow
Yashan Zhang
In this paper, we discuss diameter bound and Gromov-Hausdorff convergence of a twisted conical Kähler-Ricci flow on the total spaces of some holomorphic submersions. We also observ…
Infinite-time singularity type of the Kähler-Ricci flow
Yashan Zhang
For the Kähler-Ricci flow on a compact Kähler manifold with semi-ample canonical line bundle, we prove the singularity type at infinity does not depend on the choice of the initial…
Collapsing limits of the Kähler-Ricci flow and the continuity method
Yashan Zhang
We consider the Kähler-Ricci flow on certain Calabi-Yau fibration, which is a Calabi-Yau fibration with one dimensional base or a product of two Calabi-Yau fibrations with one dime…
The continuity method on Fano fibrations
Yashan Zhang, Zhenlei Zhang
We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a fin…
A note on conical Kähler-Ricci flow on minimal elliptic Kähler surfaces
Yashan Zhang
We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kähler-Ricci flow on a minimal elliptic Kähler surface converges in the sens…
The continuity method on minimal elliptic Kähler surfaces
Yashan Zhang, Zhenlei Zhang
We prove that, on a minimal elliptic Kähler surface of Kodaira dimension one, the continuity method introduced by La Nave and Tian in \cite{LT} starting from any initial Kähler met…