Metrics On A Surface With Bounded Total Curvature

2019/11/07 by Yuxiang Li, Li, Yuxiang, Sun Jianxin +3 · 1 citation
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.02856

openalex publication_date 2019/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let g=e^2u(dx²+dy²) be a conformal metric defined on the unit disk of C. We give an estimate of ‖∇ u‖_{L^2,∞(D_(1)/(2))} when ‖K(g)‖_L¹ is small and (μ(B_r^g(z),g))/(πr²)

Citations

• Classification of solutions of some nonlinear elliptic equations

Cited by

• Integral gradient estimates on a closed surface

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