Communications in Analysis and Geometry
Volume 26 (2018)
Optimal estimate for the gradient of Green’s function on degenerating surfaces and applications
Pages: 887 – 913
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 $L^2$-bounded second fundamental form and for Riemannian surfaces of uniformly bounded Gaussian curvature entropy.
Received 8 August 2014