Xiaohan Cai

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20232026

most citedLiouville equations on complete surfaces with nonnegative Gauss curvature

2 citations · 2 across the 4 of their papers we have counts for

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math.DG2026

Dimension of polynomial growth harmonic functions on locally conformally flat manifolds with nonnegative Ricci curvature

Xiaohan Cai, Mijia Lai

Let $H_{d} (M)$ denote the space of harmonic functions with polynomial growth of degree at most $d$ on a complete Riemannian manifold $(M, g)$ . Yau raised two fundamental que…

math.AP2026

Sharp rigidity for quasilinear Liouville equation on manifolds with nonnegative Ricci curvature

Xiaohan Cai

We study the quasilinear Liouville equation \[ -Δ_n u=e^u \] on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. Our first result shows that, if a solutio…