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In this note, we prove a Schwarz–Pick-type lemma for minimal maps between negatively curved Riemann surfaces. More precisely, we prove that if $$f:M\rightarrow N$$f:M→N is a minimal map with bounded… Click to show full abstract
In this note, we prove a Schwarz–Pick-type lemma for minimal maps between negatively curved Riemann surfaces. More precisely, we prove that if $$f:M\rightarrow N$$f:M→N is a minimal map with bounded Jacobian determinant between two complete negatively curved Riemann surfaces M and N whose sectional curvatures $$\sigma _M$$σM and $$\sigma _N$$σN satisfy $$\inf \sigma _M\ge \sup \sigma _N$$infσM≥supσN, then f is area decreasing.
Keywords:
schwarz pick;
geometry;
lemma minimal;
minimal maps;
pick lemma
Journal Title: Annals of Global Analysis and Geometry
Year Published: 2019
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Journal Title: Annals of Global Analysis and Geometry
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!