Hong Huang

activity

20062026

most citedCollapsed Manifolds With Ricci Bounded Covering Geometry

9 citations · 37 across the 31 of their papers we have counts for

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29 papers · 1 filter

math.DG2026

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 $n$ -manifold $M$ sa…

math.DG2023

Classification of compact manifolds with positive isotropic curvature

Hong Huang

We show the following result: Let $(M, g_{0})$ be a compact manifold of dimension $n \geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or…

math.DG2022★ 1 cited

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…

math.DG2022★ 1 cited

A finite Topological Type Theorem for open manifolds with Non-negative Ricci Curvature and Almost Maximal Local Rewinding Volume

Hongzhi Huang

In this paper, we present finite topological type theorems for open manifolds with non-negative Ricci curvature, under almost maximal local rewinding volume. Unlike previous relate…

math.DG2021★ 2 cited

Hessian estimates for the conjugate heat equation coupled with the Ricci flow

Hong Huang

In this short note we obtain some local and global upper bounds for the Hessian of a positive solution to the conjugate heat equation coupled with the Ricci flow.

math.DG2020★ 2 cited

Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry

Hongzhi Huang

In this work, we (partially) generalize two classical tools in study of collapsed manifolds with bounded sectional curvature: a (singular) fibration theorem by Fukaya (1987) and Ch…

math.DG2019★ 2 cited

Compact manifolds of dimension $n \geq 12$ with positive isotropic curvature

Hong Huang

We prove the following result: Let $(M, g_{0})$ be a compact manifold of dimension $n \geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, o…

math.DG2018★ 1 cited

Local derivative estimates for the heat equation coupled to the Ricci flow

Hong Huang

In this note we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang's work, we extend some…

math.DG2018★ 9 cited

Collapsed Manifolds With Ricci Bounded Covering Geometry

Hongzhi Huang, Lingling Kong, Xiaochun Rong +1

We study collapsed manifolds with Ricci bounded covering geometry i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform…

math.DG2017★ 4 cited

Kähler-Ricci flow on homogeneous toric bundles

Hong Huang

Assume that $X$ is a homogeneous toric bundle of the form $G^{C} \times_{P, τ} F$ and is Fano, where $G$ is a compact semisimple Lie group with complexification $G^\mathbb{C…

math.DG2016

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifolds

Hong Huang

We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of t…

math.DG2016

Exotic $R^{4}$ 's and positive isotropic curvature

Hong Huang

We show that no exotic $R^{4}$ admits a complete Riemannian metric with uniformly positive isotropic curvature and with bounded geometry. This is essentially a corollary of…

math.DG2015★ 1 cited

The transverse Chern-Ricci flow

Hong Huang

We introduce transverse Chern-Ricci flow for transversely Hermitian foliations, which is analogous to the Chern-Ricci flow. We show that when $F$ is homologically orienta…

math.DG2015

The Cauchy problem for fully nonlinear parabolic systems on manifolds

Hong Huang

We show the short time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabo…

math.DG2013★ 1 cited

Sasaki manifolds with positive transverse orthogonal bisectional curvature

Hong Huang

In this short note we show the following result: Let $(M^{2 n + 1}, g)$ ( $n \geq 2$ ) be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then $π_1(M…

math.DG2012★ 2 cited

Three-orbifolds with positive scalar curvature

Hong Huang

We prove the following result: Let $(O, g_{0})$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-…

math.DG2011★ 1 cited

Ricci flow on open 4-manifolds with positive isotropic curvature

Hong Huang

In this note we prove the following result: Let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential inc…

math.DG2011★ 2 cited

Four-orbifolds with positive isotropic curvature

Hong Huang

We prove the following result: Let $(X, g_{0})$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite colle…

math.DG2009★ 4 cited

Complete 4-manifolds with uniformly positive isotropic curvature

Hong Huang

We prove the following result: Let $(X, g_{0})$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite colle…

math.DG2009

Optimal transportation and monotonic quantities on evolving manifolds

Hong Huang

In this note we will adapt Topping's $L$ -optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold $(M, g_{ij} (t))$ evolving by $…

math.DG2009★ 3 cited

Backwards uniqueness of the mean curvature flow

Hong Huang

In this note we prove the backwards uniqueness of the mean curvature flow for (codimension one) hypersurfaces in a Euclidean space. More precisely, let $F_t, \widetilde{F}_t:M^n \r…

math.DG2009

Normal curvature bounds along the mean curvature flow

Hong Huang

Let $(M^{n}, g_{0})$ and $(M ˉ^{n + 1}, g ˉ)$ be complete Riemannian manifolds with $∣ \nabla ˉ^{k} R m ˉ ∣ \leq C ˉ$ for $k \leq 2$ , and suppose there is an isometric immersion…

math.DG2008

A note on the Ricci flow on noncompact manifolds

Hong Huang

Let $(M^{3}, g_{0})$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvatur…

math.DG2008

A note on K $a ¨$ hler manifolds with almost nonnegative bisectional curvature

Hong Huang

In this note we prove the following result: There is a positive constant $ε (n, Λ)$ such that if $M^{n}$ is a simply connected compact K $a ¨$ hler manifold with sectional curvature…

Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature

Classification of compact manifolds with positive isotropic curvature

Almost splitting maps, transformation theorems and smooth fibration theorems

A finite Topological Type Theorem for open manifolds with Non-negative Ricci Curvature and Almost Maximal Local Rewinding Volume

Hessian estimates for the conjugate heat equation coupled with the Ricci flow

Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry

Compact manifolds of dimension n≥12 with positive isotropic curvature

Local derivative estimates for the heat equation coupled to the Ricci flow

Collapsed Manifolds With Ricci Bounded Covering Geometry

Kähler-Ricci flow on homogeneous toric bundles

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifolds

Exotic R4's and positive isotropic curvature

The transverse Chern-Ricci flow

The Cauchy problem for fully nonlinear parabolic systems on manifolds

Sasaki manifolds with positive transverse orthogonal bisectional curvature

Three-orbifolds with positive scalar curvature

Ricci flow on open 4-manifolds with positive isotropic curvature

Four-orbifolds with positive isotropic curvature

Complete 4-manifolds with uniformly positive isotropic curvature

Optimal transportation and monotonic quantities on evolving manifolds

Backwards uniqueness of the mean curvature flow

Normal curvature bounds along the mean curvature flow

A note on the Ricci flow on noncompact manifolds

A note on Ka¨hler manifolds with almost nonnegative bisectional curvature

Compact manifolds of dimension $n \geq 12$ with positive isotropic curvature

Exotic $R^{4}$ 's and positive isotropic curvature

A note on K $a ¨$ hler manifolds with almost nonnegative bisectional curvature