Author

Shihong Zhang

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Preprint Aug 2026

Exact counting of spherical metrics with one conical singularity on rectangular tori

We prove that for every integer $n\geq 2$ and $8\pi(n-1)<\rho<8\pi n$, the singular Liouville equation $\Delta u+\e^u=\rho\delta_0$ on a rectangular torus $E_{\mathrm{i}b}=\mathbb{C}/(\mathbb Z+\mathrm{i} b\mathbb Z)$ has exactly $n$ solutions, which are all axisymmetric. Together with previous results by Chen-Lin and...

Zhi-Jie Chen, Shi-Hong Zhang · 0 citations

Preprint Aug 2026

Conformal Metrics on the unit Ball with Constant $Q$-Curvature, Constant $T$-Curvature, and Minimal Boundary

We completely classify conformal metrics on the unit ball $(\mathbb{B}^{n+1},|\mathrm{d} x|^2)$, $n\geq4$, with positive constant $Q$-curvature, positive constant $T$-curvature, and minimal boundary. After normalizing the $Q$-curvature, there is a unique conformal metric for each $T$-curvature value in $[0,+\infty)$, u...

Li-Ming Sun, Heming Wang, Shi-Hong Zhang · 0 citations