1 citations · 1 across the 10 of their papers we have counts for
10 papers
Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature
Jiangcheng You, Heng Zhang
We prove that a contractible -manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to . We also prove that, if the interior $M_…
Uniform Comparison of Hyperbolic Ball Volumes on the Universal Cover
Heng Zhang
Let denote the simplicial volume of , , and denotes hyperbolic -space. We prove that, i…
Reciprocal sums of Neumann eigenvalues in non-Euclidean space forms
Jiangcheng You, Heng Zhang
Let be the simply connected space form of dimension and constant sectional curvature . For every bounded connected smooth domain , ass…
Arbitrarily Many Non-degenerate Local Maxima of First Nonzero Eigenfunctions on Positively Curved Two-spheres
Heng Zhang
We prove that, for every integer , there is a smooth closed Riemannian surface diffeomorphic to , with positive Gaussian curvature, such that …
Gromov's Euclidean Endpoint Rigidity for the Positive Mass Theorem
Jiangcheng You, Heng Zhang
We prove Gromov's Euclidean endpoint rigidity conjecture. Let be a smooth complete metric on with non-negative scalar curvature. If $$ |g-g_{\Euc}|=o(r^{-1}),\qqua…
On Lichnerowicz sharp distance-regular graphs
Kaizhe Chen, Shiping Liu, Heng Zhang
The first non-zero Laplacian eigenvalue of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature . This is a discrete analogue of the classical Lichnerowic…
Existence results for Tzitzéica equation via topological degree method on graphs
Kaizhe Chen, Heng Zhang
We derive some existence results for the solutions of the Tzitzéica equation \begin{equation*} -Δu + h_1(x)e^{Au} + h_2(x)e^{-Bu}=0 \end{equation*} and the generalized Tzitzéica eq…
Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter
Shiping Liu, Heng Zhang
We prove the monotonic normalized heat diffusion property on distance-regular graphs with classical parameters of diameter . Regev and Shinkar found a Cayley graph for which thi…
Ricci curvature, diameter and eigenvalues of amply regular graphs
Kaizhe Chen, Chunyang Hu, Shiping Liu +1
Amply regular graphs are graphs with local distance-regularity constraints. In this paper, we prove a weaker version of a conjecture proposed by Qiao, Park, and Koolen on diameter…
Curvature and local matchings of conference graphs and extensions
Kaizhe Chen, Shiping Liu, Heng Zhang
We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters . Ou…