Mijia Lai

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20232026

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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…

math.AP2023

Liouville equations on complete surfaces with nonnegative Gauss curvature

Xiaohan Cai, Mijia Lai

We study finite total curvature solutions of the Liouville equation $Δ u + e^{2 u} = 0$ on a complete surface $(M, g)$ with nonnegative Gauss curvature. It turns out that the asymptotic b…