Heng Zhang

collaborators

10 papers

math.DG2026

Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature

Jiangcheng You, Heng Zhang

We prove that a contractible $3$ -manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to $R^{3}$ . We also prove that, if the interior $M_…

math.DG2026

Uniform Comparison of Hyperbolic Ball Volumes on the Universal Cover

Heng Zhang

Let $∥ M ∥_{I^} $ denote the simplicial volume of $M$ , $V_{r} (X, h) = sup_{x \in X} Vol_{h} (B_{h} (x, r))$ , and $H^{n}$ denotes hyperbolic $n$ -space. We prove that,…

math.DG2026

Reciprocal sums of Neumann eigenvalues in non-Euclidean space forms

Jiangcheng You, Heng Zhang

Let $M_{I^}^{n} º$ be the simply connected space form of dimension $n \geq 2$ and constant sectional curvature $I^º \in {- 1, 1}$ . For every bounded connected smooth domain $I^c ◯ \subset M_{I^}^{n} º$ ,…

math.DG2026

Arbitrarily Many Non-degenerate Local Maxima of First Nonzero Eigenfunctions on Positively Curved Two-spheres

Heng Zhang

We prove that, for every integer $m \geq 2$ , there is a smooth closed Riemannian surface $(M, g)$ diffeomorphic to $S^{2}$ , with positive Gaussian curvature, such that $I^»_{1} (M)$ …

math.DG2026

Gromov's Euclidean Endpoint $C^{0}$ Rigidity for the Positive Mass Theorem

Jiangcheng You, Heng Zhang

We prove Gromov's Euclidean endpoint $C^{0}$ rigidity conjecture. Let $g$ be a smooth complete metric on $R^{3}$ with non-negative scalar curvature. If $$ |g-g_{\Euc}|=o(r^{-1}),\qqua…

math.CO2026

On Lichnerowicz sharp distance-regular graphs

Kaizhe Chen, Shiping Liu, Heng Zhang

The first non-zero Laplacian eigenvalue $I^»_{1}$ of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature $I^º$ . This is a discrete analogue of the classical Lichnerow…

Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature

Uniform Comparison of Hyperbolic Ball Volumes on the Universal Cover

Reciprocal sums of Neumann eigenvalues in non-Euclidean space forms

Arbitrarily Many Non-degenerate Local Maxima of First Nonzero Eigenfunctions on Positively Curved Two-spheres

Gromov's Euclidean Endpoint C0 Rigidity for the Positive Mass Theorem

On Lichnerowicz sharp distance-regular graphs

Gromov's Euclidean Endpoint $C^{0}$ Rigidity for the Positive Mass Theorem