1 citations · 4 across the 8 of their papers we have counts for
8 papers
Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature
Hongzhi Huang, Xian-Tao Huang, Jikang Wang +1
In this paper, we prove fibration theorems for manifolds with almost nonnegative Ricci curvature and certain extra regularity assumptions. We show that a closed -manifold sa…
Almost splitting maps, transformation theorems and smooth fibration theorems
Hongzhi Huang, Xian-Tao Huang
In this paper, we introduce a notion, called generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature bounded…
Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature
Xian-Tao Huang
Suppose is a Riemannian manifold having dimension , nonnegative Ricci curvature, maximal volume growth and unique tangent cone at infinity. In this case, the tangent con…
On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth
Xian-Tao Huang
Suppose is a Riemannian manifold with nonnegative Ricci curvature, and let be the dimension of the space of harmonic functions with polynomial growth of grow…
Noncompact RCD(0,N) spaces with linear volume growth
Xian-tao Huang
Since non-compact RCD(0, N) spaces have at least linear volume growth, we study noncompact RCD(0, N) spaces with linear volume growth in this paper. One of the main results is that…
Path-connectedness of the moduli spaces of metrics with positive isotropic curvature on four-manifolds
Bing-Long Chen, Xian-Tao Huang
In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.
A note on the positivity of a quasi-local mass in general dimensions
Xian-Tao Huang
Wang and Yau [10] introduced a quasi-local mass, which is a hyperbolic background generalization of Liu-Yau's expression [7] [8], and proved its positivity. In this note, we prove…
A Simple Method for the Optimal Transportation
Xian-Tao Huang
In this paper we will give a new proof of the monotonicity of Wasserstein distances of two diffusions under super Ricci flow. Our proof is based on the coupling method of B.Andrew…