collaborators

6 papers

math.DG2026

Immersed hypersurfaces with positive first Newton transformation

Jiangcheng You, Heng Zhang

We prove that every closed cooriented hypersurface immersion in , , with positive definite first Newton transformation bounds a compact immersed manifold with the…

math.DG2026

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_…

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 be the simply connected space form of dimension and constant sectional curvature . For every bounded connected smooth domain , ass…

math.DG2026

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…

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…