arXiv subjects

Chiyu Zhou

Publications and source records attributed to Chiyu Zhou.

5 recordsLinked to original sources

arXiv2026

Structure theorems for Lichnerowicz-sharp graphs

Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. Let $G$ be a finite, connected, simple, unweighted graph with Bakry--\'Emery curvature bounded below by $K$. We call $G$ Lichnerowicz-sharp if its first non-zero non-normalized Laplacian eigenvalue $\lambda_1=K$. We prove that, after removing a canonical collection of edges on which every $K$-eigenfunction is constant, the resulting graph has a canonical bundle structure. Its fibers are regular, have similar structure with hypercubes, and are Laplacian-cospectral with hypercubes, although they need not themselves be hypercubes. If the base graph is nontrivial, then it satisfies $\mathrm{CD}(K,\infty)$ and has first eigenvalue strictly greater than $K$. As a consequence, if the vertex degree in $G$ is constant along each canonical fiber, then every fiber is a hypercube and $G$ is a hypercube bundle. Conversely, for every $d\geq 4$, we construct Lichnerowicz-sharp graphs with non-hypercube canonical fibers of degree $d$.

math.DG↗

arXiv2026

Pointwise subexponential growth and near-diffusive displacement on bounded-degree graphs with non-negative Ollivier--Ricci curvature

Let $G=(V,E)$ be a possibly infinite, locally finite graph with non-negative Ollivier--Ricci curvature and degrees bounded by $d<\infty$. We prove that there exists a constant $C_d$ such that the continuous-time random walk displacement and log-volume growth satisfy \[ \mathbb{E}_x \mathrm{dist}(x,X_t)^2 \le t \exp\left[C_d \sqrt{\log t \log\log t}\right], \] \[ \log \mathrm{Vol}(B(x,r)) \le \exp\left[C_d \sqrt{\log r \log\log r}\right], \] for every $x\in V$ and all $r,t \ge e^e$.

math.DG↗

arXiv2026

Regular Lichnerowicz-sharp graphs are hypercube bundles

Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. Let $G$ be a finite, connected, simple, unweighted graph with Bakry--\'Emery curvature bounded below by $K$. We call $G$ Lichnerowicz-sharp if its first non-zero non-normalized Laplacian eigenvalue $\lambda_1=K$. We prove that all regular Lichnerowicz-sharp graphs are hypercube bundles with constant Bakry-\'Emery curvature $2$. A hypercube bundle is a graph bundle whose fiber graphs are hypercubes. As applications, we show that any $d$-regular Lichnerowicz-sharp graph with the multiplicity $m_K(G)$ of $\lambda_1=K$ at least $d/2$ can split off a hypercube of certain dimension. Moreover, we characterize all $d$-regular Lichnerowicz-sharp graphs with $m_{K}(G)\geq d-3$. Interestingly, our result leads to the following spectral rigidity theorem of hypercubes. For a graph $G$ with maximum degree $\Delta$, if the multiplicity $m_K(G)\geq \Delta-1$, then $G$ is a $\Delta$-dimensional hypercube. This improves, in the unweighted setting, the multiplicity condition $m_K(G)\geq \Delta$ appearing in the hypercube rigidity theorem of Liu, M\"unch, and Peyerimhoff. This improvement is optimal.

math.DG↗

arXiv2025

Quantitative Obata's theorem in discrete setting

Under mild assumptions, we show that a connected weighted graph $G$ with lower Ricci curvature bound $K>0$ in the sense of Bakry-\'Emery and the $d$-th non-zero Laplacian eigenvalue $\lambda_d$ close to $K$, with $d$ being the maximal combinatorial vertex degree of $G$, has an underlying combinatorial structure of the $d$-dimensional hypercube graph. Moreover, such a graph $G$ is close in terms of Frobenius distance to a properly weighted hypercube graph. Furthermore, we establish their closeness in terms of eigenfunctions. Our results can be viewed as discrete analogies of the almost rigidity theorem and quantitative Obata's theorem on Rimennian manifolds.

math.DG↗

arXiv2024

Design of ANF/MXene/SSG sandwich structure with electromagnetic shielding performance and impact resistance

Since entering the information era, electronic devices gradually play an important role in daily lives. However, the abuse of electronic devices leads to corresponding electromagnetic EM wave pollution. The complex external environment causes the potential for physical impact. In this work, an ANF MXene SSG flexible sandwich structure was fabricated according to methods of vacuum filtration, directional freeze-casting solidification, and polyurethane encapsulation. Apart from its excellent protection function, the sandwich structure also acts as a human body movement sensor.

physics.app-ph↗