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Publications (28)

math.DG2026

Homological $k$ -systole in $n$ -manifolds with positive intermediate curvature

Jingche Chen, Han Hong

In this paper, we prove optimal $k$ -systolic inequalities and characterize the case of equality on closed $n$ -dimensional Riemannian manifolds with positive intermediate curvature…

math.MG2017

The $p$ -capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems

Han Hong, Deping Ye, Ning Zhang

In this paper, combining the $p$ -capacity for $p \in (1, n)$ with the Orlicz addition of convex domains, we develop the $p$ -capacitary Orlicz-Brunn-Minkowski theory. In particular,…

math.DG2026

A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary

Han Hong, Gaoming Wang

We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension $n \geq 2$ has $Î»_1(-Î±Î+\ope…

math.FA2017

Sharp geometric inequalities for the general $p$ -affine capacity

Han Hong, Deping Ye

In this article, we propose the notion of the general $p$ -affine capacity and prove some basic properties for the general $p$ -affine capacity, such as affine invariance and monoton…

econ.EM2026

Statistical Inference of Optimal Allocations I: Regularities and their Implications

Kai Feng, Han Hong, Denis Nekipelov

In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions t…

math.MG2016

The Orlicz-Petty bodies

Baocheng Zhu, Han Hong, Deping Ye

This paper is dedicated to the Orlicz-Petty bodies. We first propose the homogeneous Orlicz affine and geominimal surface areas, and establish their basic properties such as homoge…

math.ST2008

Semiparametric efficiency in GMM models with auxiliary data

Xiaohong Chen, Han Hong, Alessandro Tarozzi

We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary d…

math.ST2020

Bayesian Indirect Inference and the ABC of GMM

Michael Creel, Jiti Gao, Han Hong +1

In this paper we propose and study local linear and polynomial based estimators for implementing Approximate Bayesian Computation (ABC) style indirect inference and GMM estimators.…

math.DG2026

Spectral splitting theorem and ends of minimal hypersurfaces

Han Hong, Gaoming Wang

In this paper, we give a new proof of the splitting theorem on manifolds with nonnegative spectral Ricci curvature proved in [APX24, CMMR24, HW26]. Furthermore, by constructing wei…

math.DG2025

Rigidity of CMC hypersurfaces in 5-and 6-manifolds

Han Hong, Zetian Yan

We prove that nonnegative $3$ -intermediate Ricci curvature combined with uniformly positive $k$ -triRic curvature implies rigidity of complete noncompact two-sided stable minimal hy…

math.DG2023

Large Steklov eigenvalues on hyperbolic surfaces

Xiaolong Hans Han, Yuxin He, Han Hong

In this paper, we first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue $I ¨ ~ _{1}$ tends to infinit…

econ.EM2023

An MCMC Approach to Classical Estimation

Victor Chernozhukov, Han Hong

This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributi…

stat.ME2019

Decision Making with Machine Learning and ROC Curves

Kai Feng, Han Hong, Ke Tang +1

The Receiver Operating Characteristic (ROC) curve is a representation of the statistical information discovered in binary classification problems and is a key concept in machine le…

math.DG2026

Intermediate curvature and splitting theorem

Jingche Chen, Han Hong

In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3 \leq n \leq 5$ , $1\leq m\leq…

math.DG2025

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Jingche Chen, Han Hong

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with bound…

math.DG2021

Capillary surfaces: stability, index and curvature estimates

Han Hong, Artur B. Saturnino

In this paper we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immerse…

math.DG2025

Do Carmo's problem for CMC hypersurfaces in $R^{6}$

Jingche Chen, Han Hong, Haizhong Li

In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in $R^{6}$ with finite index must be minimal. This provides a positive answer to do Ca…

math.DG2025

A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary

Han Hong, Gaoming Wang

We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) ha…

math.DG2023

Asymptotic Plateau problem via equidistant hyperplanes

Han Hong, Haizhong Li, Meng Zhang

We show the existence of a complete, strictly locally convex hypersurface within $H^{n + 1}$ that adheres to a curvature equation applicable to a broad range of curvature fu…

econ.EM2024

Statistical Tests for Replacing Human Decision Makers with Algorithms

Kai Feng, Han Hong, Ke Tang +1

This paper proposes a statistical framework of using artificial intelligence to improve human decision making. The performance of each human decision maker is benchmarked against t…

math.SP2020

Higher dimensional surgery and Steklov eigenvalues

Han Hong

We show that for compact Riemannian manifolds of dimension at least $3$ with nonempty boundary, we can modify the manifold by performing surgeries of codimension $2$ or higher, whi…

cs.LG2026

Integrating Unstructured Text into Causal Inference: Empirical Evidence from Real Data

Boning Zhou, Ziyu Wang, Han Hong +1

Causal inference, a critical tool for informing business decisions, traditionally relies heavily on structured data. However, in many real-world scenarios, such data can be incompl…

math.DG2025

CMC hypersurface with finite index in hyperbolic space $H^{4}$

Han Hong

In this paper, we prove that there are no complete noncompact constant mean curvature hypersurfaces with the mean curvature $H > 1$ , finite index and finite topology in hyperbolic…

math.DG2024

On $I^´$ -Stable Minimal Hypersurfaces in $R^{n + 1}$

Han Hong, Haizhong Li, Gaoming Wang

In this paper, we extend several results established for stable minimal hypersurfaces to $I^´$ -stable minimal hypersurfaces. These include the regularity and compactness theorems fo…

math.DG2025

Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology

Nicolau S. Aiex, Han Hong

We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the $C^{k}$ graphical sense away from a finite set o…

math.DG2019

Index Estimates for Surfaces with Constant Mean Curvature in $3$ -dimensional Manifolds

Nicolau S. Aiex, Han Hong

We prove index estimates for closed and free boundary CMC surfaces in certain $3$ -dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are a…

cs.CV2026

FoMoVLA: Bridging Visual Foresight and Motion Guidance for Vision-Language-Action Models

Wei Li, Peijin Jia, Yuan Ma +9

FoMoVLA enhances vision-language-action models by jointly predicting future visual features and tracking sparse 2D points, providing both goal states and motion paths to improve co…

#vision-language-action#visual foresight#motion guidance#sparse point tracking

math.DG2024

Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $H^{n + 1}$

Han Hong, Ruijia Zhang

In this paper, we consider the asymptotic $I ¨ _{k}$ Plateau problem in hyperbolic space. We establish $C^{2}$ estimates for semi-convex complete hypersurfaces satisfying constant $I ¨ _{k}$ …

Publications (28)

Homological k-systole in n-manifolds with positive intermediate curvature

The p-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems

A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary

Sharp geometric inequalities for the general p-affine capacity

Statistical Inference of Optimal Allocations I: Regularities and their Implications

The Orlicz-Petty bodies

Semiparametric efficiency in GMM models with auxiliary data

Bayesian Indirect Inference and the ABC of GMM

Spectral splitting theorem and ends of minimal hypersurfaces

Rigidity of CMC hypersurfaces in 5-and 6-manifolds

Large Steklov eigenvalues on hyperbolic surfaces

An MCMC Approach to Classical Estimation

Decision Making with Machine Learning and ROC Curves

Intermediate curvature and splitting theorem

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Capillary surfaces: stability, index and curvature estimates

Do Carmo's problem for CMC hypersurfaces in R6

A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary

Asymptotic Plateau problem via equidistant hyperplanes

Statistical Tests for Replacing Human Decision Makers with Algorithms

Higher dimensional surgery and Steklov eigenvalues

Integrating Unstructured Text into Causal Inference: Empirical Evidence from Real Data

CMC hypersurface with finite index in hyperbolic space H4

On I^´-Stable Minimal Hypersurfaces in Rn+1

Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology

Index Estimates for Surfaces with Constant Mean Curvature in 3-dimensional Manifolds

FoMoVLA: Bridging Visual Foresight and Motion Guidance for Vision-Language-Action Models

Curvature estimates for semi-convex solutions of asymptotic Plateau problem in Hn+1

Homological $k$ -systole in $n$ -manifolds with positive intermediate curvature

The $p$ -capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems

Sharp geometric inequalities for the general $p$ -affine capacity

Do Carmo's problem for CMC hypersurfaces in $R^{6}$

CMC hypersurface with finite index in hyperbolic space $H^{4}$

On $I^´$ -Stable Minimal Hypersurfaces in $R^{n + 1}$

Index Estimates for Surfaces with Constant Mean Curvature in $3$ -dimensional Manifolds

Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $H^{n + 1}$