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arXiv · 1307.5425

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

Paul Laurain·Tristan Rivière
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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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Paul Laurain, Tristan Rivière. 2013-07-20. Optimal estimate for the gradient of Green functions on degenerating surfaces and applications. https://arxiv.org/abs/1307.5425

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