Author

Qi-Xuan Hu

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Preprint Sep 2026

Scalar curvature growth on nonnegatively curved three-manifolds

Let $(M^3,g)$ be a complete, connected, noncompact Riemannian three-manifold without boundary and with nonnegative sectional curvature. We prove that its scalar-curvature integral over geodesic balls, divided by the radius, has a limit. In the one-ended case, \[ \lim_{r\to\infty}\frac1r\int_{B_p(r)}\operatorname{Scal}\...

Qi-Xuan Hu · 0 citations

Preprint Sep 2026

A quadratic comparison of Neumann eigenvalues on thin convex domains in arbitrary dimenstion

Let $\Omega\subset\mathbb R^n$ be a bounded convex domain that is thin around a chosen diameter segment. We compare its Neumann spectrum with the spectrum of that segment weighted by the $(n-1)$-dimensional volumes of its perpendicular sections. We prove an $O(\varepsilon^2)$ comparison of the mean-zero inverse operato...

Qi-Xuan Hu · 0 citations