Optimal estimate for the gradient of Green functions on degenerating surfaces and applications

2013/07/20 by Paul Laurain, Laurain, Paul, Tristan Rivière +1 · 1 citation
Computer Science · Mathematics · #30F10 #32G15 #35J35 #53A05 #53A30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1307.5425

openalex publication_date 2013/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a uniform estimate for the gradient of the Green function on a closed Riemann surface, independent of its conformal class, and we derive compactness results for immersions with L2-bounded second fundamental form and for riemannian surfaces of uniformly bounded gaussian curvature entropy.

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• Integral gradient estimates on a closed surface

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