Jintian Zhu

A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound

Tianze Hao, Jintian Zhu

A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that $R \to \infty lim sup \frac{1}{R} \int_{B (p, R)} S c a l d V = + \infty.$ The constructio…

Positive Scalar Curvature Obstructions via Singular Dimension Descent

Yuchen Bi, Jintian Zhu

In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau ty…

Curvature-free effects from volume growth and ends-counting and their applications

Yuchen Bi, Jintian Zhu

In this paper, we investigate two curvature-free effects from volume growth and ends-counting, respectively. Motivated by generalizing classical results from Ricci curvature to oth…

Riemannian Penrose inequality in all dimensions

Yuchen Bi, Jintian Zhu

We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing m…

A proof for the Riemannian positive mass theorem up to dimension 19

Yuchen Bi, Tianze Hao, Shihang He +2

In this paper, we prove the Riemannian positive mass theorem up to dimension $19$ , building on a combination of torical symmetrization and the singularity blow-up technique develop…

On diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature

Jianchun Chu, Man-Chun Lee, Jintian Zhu

In this paper, we establish some diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature.

Mass-capacity inequality modeled on conformally flat manifolds

Yuchen Bi, Jintian Zhu

In the spin case, we can establish a mass-capacity inequality for generalized asymptotically flat manifolds $(M, g, E)$ with nonnegative scalar curvature, where the equality implies…

Existence of Constant Mean Curvature Surfaces in Asymptotically Flat and Asymptotically Hyperbolic Manifolds

Liam Mazurowski, Jintian Zhu

We prove the existence of compact surfaces with prescribed constant mean curvature in asymptotically flat and asymptotically hyperbolic manifolds. More precisely, let $(M^{3}, g)$ be…

Interior control for surfaces with positive scalar curvature and its application

Shuli Chen, Jianchun Chu, Jintian Zhu

Let $M^{n}$ , $n \in {3, 4, 5}$ , be a closed aspherical $n$ -manifold and $S \subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly…

Homological $n$ -systole in $(n + 1)$ -manifolds and bi-Ricci curvature

Jianchun Chu, Man-Chun Lee, Jintian Zhu

In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes t…

On Kähler manifolds with non-negative mixed curvature

Jianchun Chu, Man-Chun Lee, Jintian Zhu

In this work, we investigate compact Kähler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional cu…

Optimal volume bound and volume growth for Ricci-nonnegative manifolds with positive Bi-Ricci curvature

Jie Zhou, Jintian Zhu

In this paper, we prove the optimal volume growth for complete Riemannian manifolds $(M^{n}, g)$ with nonnegative Ricci curvature everywhere and bi-Ricci curvature bounded from below…

Llarull's theorem on punctured sphere with $L^{\infty}$ metric

Jianchun Chu, Man-Chun Lee, Jintian Zhu

The classical Llarull theorem states that a smooth metric on $n$ -sphere cannot have scalar curvature no less than $n (n - 1)$ and dominate the standard spherical metric at the same ti…

On open manifolds admitting no complete metric with positive scalar curvature

Yuguang Shi, Jian Wang, Runzhang Wu +1

In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition f…