Xiaohan Cai

collaborators

3 papers

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…

math.AP2024

An area growth estimate of the Liouville equation

Xiaohan Cai, Mijia Lai, Chilin Zhang

We establish an area growth estimate for solutions that are bounded from above of the Liouville equation $Δ u + K e^{2 u} = 0$ with a positive pinched curvature $0 < λ \leq K \leq Λ$ . As an a…