Author

Haoxuan Cheng

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Preprint Sep 2026

Unbounded normalized scalar curvature integrals in dimension four

We give counterexamples to Yau's question on normalized scalar curvature integrals in every dimension $n\geq4$. For each such $n$, there exists a smooth complete Riemannian metric $g$ on $\mathbb{R}^n$ with nonnegative Ricci curvature and a pole such that \[ \lim_{R\to\infty}R^{2-n}\int_{B_q(R)}\mathrm{Scal}_g\,\mathrm...

Hao-Xuan Cheng · 2 citations

Preprint Sep 2026

Singular Rotational Self-Similar Tori for Odd $\sigma_k$-Curvature Flows

For every pair of integers $3\leq k<n$ with $k$ odd, we construct a compact embedded rotational torus in $\mathbb{R}^{n+1}$ whose homothetic dilations satisfy the unnormalised $\sigma_k$-curvature flow in a Sobolev almost-everywhere sense. Its profile curve has H\"older regularity $C^{1,1/k}$ and Sobolev regularity $W^...

Hao-Xuan Cheng, Jun-Qi Lai, Guo-Xin Wei · 0 citations