Author

Hao Xu

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Preprint Nov 2026

A proof of the spectral rigidity for complex projective space

We give a proof of a folklore conjecture that a compact K\"ahler manifold with the same scalar Laplace spectrum as complex projective space equipped with the Fubini--Study metric is holomorphically isometric to it. More generally, we prove that the spectrum of the Hodge Laplacian in any one fixed degree $p$ determines...

Ke-Feng Liu, Hao Xu · 0 citations

Preprint Oct 2026

Uniform asymptotics and the Weil--Petersson constant

In their celebrated work on the large-genus asymptotic expansion of Weil--Petersson volumes, Mirzakhani and Zograf left open the question of whether the Weil--Petersson constant satisfies $C_{\mathrm{WP}}=\pi^{-1/2}$. We resolve the conjecture affirmatively. Our strategy is to consider a family of spectral curves inter...

Ke-Feng Liu, Hao Xu · 0 citations