2 papers
math.AP2026
Arbitrary Dirichlet Eigenvalue Multiplicities on Smooth Star-Shaped Euclidean Domains
Zhijie Chen, Chen-Gang Long, Shihong Zhang
In every fixed dimension \(N\ge3\), for any finite list of positive integers \(m_1,\ldots,m_\ell\), we construct smooth strictly star-shaped Euclidean domains whose first \(\ell+1\…
math.AP2026
Exact counting of spherical metrics with one conical singularity on rectangular tori
Zhijie Chen, Shihong Zhang
We prove that for every integer and , the singular Liouville equation $Δu+\e^u=ρδ_0$ on a rectangular torus $E_{\mathrm{i}b}=\mathbb{C}/(\mathbb Z+\mathrm{…