arXiv subjects

Huaiyu Zhang

Publications and source records attributed to Huaiyu Zhang.

7 recordsLinked to original sources

arXiv2026

Evidence for monopole-like topological magnetoelectric effect in image potential states

Magnetic monopoles, hypothetical particles behaving as isolated magnetic charges, have long been predicted by theories beyond the standard model but remain elusive in experimental detection. Subsequently, Xiaoliang Qi et al. proposed that magnetic monopoles can be constructed in real space by introducing an active electric field at the interface between a topological insulator and vacuum [Science 323, 1184 (2009)]. Here we use scanning tunneling microscopy in the field-emission regime to realize an active electric-field geometry at the surface of the higher-order topological insulator Bi(111), and observe an anomalous splitting of the image potential states (IPSs). By tuning the dielectric properties of the substrate and film thickness, we considered that the peak-splitting of IPSs is related to the radially active electric field and topological surface states. Combined with phenomenological analysis, this peaksplitting can be attributed to the equivalent magnetic field of monopole-like topological magnetoelectric response. This work establishes field-emission IPS spectroscopy as a sensitive platform for generating active electric fields and probing the resulting image magnetic monopoles at topological surfaces.

cond-mat.mtrl-sci↗

arXiv2024

Rigidity of eigenvalues of shrinking Ricci solitons

In this paper, we study the rigidity of eigenvalues of shring Ricci solitons. It is known that the drifted Laplacian on shrinking Ricci solitons has discrete spectrum, its eigenvalues have a lower bound and a rigidity result holds. Firstly, we show that if the $n^\text{th}$ eigenvalue is close to this lower bound, then the $n$-soliton must be the trivial Gaussian soliton $\mathbb{R}^n$. Secondly, we show similar results for the $(n-1)^\text{th}$ and $(n-2)^\text{th}$ eigenvalue under a non-collapsing condition. Lastly, we give an alomost rigidity for the $k^\text{th}$ eigenvalue with general $k$. Part of our results could be viewed as an soliton (could be noncompact) analog of Theorem 1.1 (which only holds for compact manifolds) in Peterson (Invent. Math. 138 (1999): 1-21).

math.DG↗

arXiv2024

On the scalar curvature rigidity for mainifolds with non-positive Yamabe invariant

In this paper, we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant. We prove that if the scalar curvature is not less than the Yamabe invariant in distributional sense, then the manifold must be isometric to an Einstein manifold. This result extends Theorem 1.4 in Jiang, Sheng and the first author (Sci. China Math. 66 (2023) no. 6, 1141-1160), from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant. This result depends highly on an analysis and estimates of geometric evolution equations.

math.AP↗

arXiv2024

The Penrose Inequality for Metrics with Singular Sets

We study the Penrose inequality and its rigidity for metrics with singular sets. Our result could be viewed as a complement of Theorem 1.1 of Lu and Miao (J. Funct. Anal. 281, 2021) and Theorem 1.2 of Shi, Wang and Yu (Math. Z. 291, 2019), in which they assume the singular set is a hypersurface and assume an additional condition on the mean curvature. As a complement, this paper study the case of singular set of dimensional less than n-1, without any additional conditions.

math.DG↗

arXiv2021

Weak scalar curvature lower bounds along Ricci flow

In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in distributional sense provided that the initial metric is $W^{1,p}$ for some $n<p\le \infty$. As an application, we use this result to study the relation between Yamabe invariant and Ricci flat metrics. We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in distributional sense, then the manifold is isometric to a Ricci flat manifold.

math.DG↗

arXiv2020

Removable singularity of positive mass theorem with continuous metrics

In this paper, we consider asymptotically flat Riemannnian manifolds $(M^n,g)$ with $C^0$ metric $g$ and $g$ is smooth away from a closed bounded subset $Σ$ and the scalar curvature $R_g\ge 0$ on $M\setminus Σ$. For given $n\le p\le \infty$, if $g\in C^0\cap W^{1,p}$ and the Hausdorff measure $\mathcal{H}^{n-\frac{p}{p-1}}(Σ)<\infty$ when $n\le p<\infty$ or $\mathcal{H}^{n-1}(Σ)=0$ when $p=\infty$, then we prove that the ADM mass of each end is nonnegative. Furthermore, if the ADM mass of some end is zero, then we prove that $(M^n,g)$ is isometric to the Euclidean space by showing the manifold has nonnegative Ricci curvature in RCD sense. This extends the result of [Lee-LeFloch2015] from spin to non-spin, also improves the result of [Shi-Tam2018] and [Lee2013]. Moreover, for $p=\infty$, this confirms a conjecture of Lee [Lee2013].

math.DG↗

arXiv2018

Localizing and Quantifying Damage in Social Media Images

Traditional post-disaster assessment of damage heavily relies on expensive GIS data, especially remote sensing image data. In recent years, social media has become a rich source of disaster information that may be useful in assessing damage at a lower cost. Such information includes text (e.g., tweets) or images posted by eyewitnesses of a disaster. Most of the existing research explores the use of text in identifying situational awareness information useful for disaster response teams. The use of social media images to assess disaster damage is limited. In this paper, we propose a novel approach, based on convolutional neural networks and class activation maps, to locate damage in a disaster image and to quantify the degree of the damage. Our proposed approach enables the use of social network images for post-disaster damage assessment and provides an inexpensive and feasible alternative to the more expensive GIS approach.

cs.CV↗