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arXiv · 1904.00487

A Schwarz-Pick lemma for minimal maps

Andreas Savas-Halilaj
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Abstract

In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved Riemann surfaces M and N whose sectional curvatures $\sigma_M$ and $\sigma_N$ satisfy $inf\sigma_M \ge sup\sigma_N$, then f is area decreasing.

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Andreas Savas-Halilaj. 2019-03-31. A Schwarz-Pick lemma for minimal maps. https://arxiv.org/abs/1904.00487

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