English

A Schwarz-Pick lemma for minimal maps

Differential Geometry 2019-04-02 v1

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:MNf:M \to N is a minimal map with bounded Jacobian between two complete negatively curved Riemann surfaces M and N whose sectional curvatures σM\sigma_M and σN\sigma_N satisfy infσMsupσNinf\sigma_M \ge sup\sigma_N, then f is area decreasing.

Keywords

Cite

@article{arxiv.1904.00487,
  title  = {A Schwarz-Pick lemma for minimal maps},
  author = {Andreas Savas-Halilaj},
  journal= {arXiv preprint arXiv:1904.00487},
  year   = {2019}
}
R2 v1 2026-06-23T08:24:36.459Z