Jiangcheng You

collaborators

5 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

Intrinsic Brown--York Type Mass at Infinity in Four Dimensions

Jiangcheng You

We study a Brown--York type mass for closed hypersurfaces in four-dimensional asymptotically flat manifolds. The reference mean curvature is defined intrinsically as the trace of t…

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

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.DG2026

Curvature at infinity of scalar-flat ALE four-manifolds

Jiangcheng You

We study refined asymptotics of scalar-flat ALE four-manifolds in the Tian--Viaclovsky setting, namely for self-dual or anti-self-dual metrics and for metrics with harmonic curvatu…

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

Intrinsic Brown--York Type Mass at Infinity in Four Dimensions

Reciprocal sums of Neumann eigenvalues in non-Euclidean space forms

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

Curvature at infinity of scalar-flat ALE four-manifolds

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