Author

Jin-Tian Zhu

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Preprint Oct 2026

Uniform positive scalar curvature from supercritical quadratic decay

Let $(M^n,g)$ be a complete connected noncompact smooth Riemannian manifold without boundary, with $n\ge3$ and positive scalar curvature. We prove that $M$ admits a complete smooth metric of uniformly positive scalar curvature if $$ \liminf_{d_g(o,x)\to\infty}d_g(o,x)^2R_g(x)>\frac{n-1}{n} $$ for a fixed point $o\in M$...

Zhe-Hui Wang, Jin-Tian Zhu · 1 citation

Preprint Sep 2026

The metric extension problem under positive and negative curvature conditions

We first prove that every smooth boundary metric on a compact manifold extends to a metric with any prescribed positive lower bound for Ricci curvature, whereas extensions under stronger positive $k^{\mathrm{th}}$-intermediate Ricci curvature conditions may fail due to local obstructions. For negative sectional curva...

Wen-Long Wang, Jin-Tian Zhu · 0 citations

Preprint Sep 2026

Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven

Let $4\le n\le7$ and let $(M^n,g)$ be a complete, connected, orientable, noncompact Riemannian manifold of positive scalar curvature. We prove that if the asymptotic quadratic scalar curvature coefficient of $g$ is greater than $(n-1)/n$, then $M$ carries a complete smooth metric whose scalar curvature is at least one....

Zhe-Hui Wang, Jin-Tian Zhu · 4 citations · ⚡2