Curvature estimate on an open Riemann surface with the induced metric

DOI10.1007/s00209-020-02615-4zbMath1470.32040OpenAlexW3087462725MaRDI QIDQ2031719

Min Ru, Xingdi Chen, Zhi-Xue Liu, Ye-Zhou Li

Publication date: 10 June 2021

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-020-02615-4

zbMATH Keywords

Riemann surfacesholomorphic mapsconformal metricGauss curvaturenormal family

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Other generalizations of function theory of one complex variable (32A30) Value distribution theory in higher dimensions (32H30)

Related Items

The value distribution of Gauss maps of immersed harmonic surfaces with ramification ⋮ Picard-type theorem and curvature estimate on an open Riemann surface with ramification

Cites Work

• On the maximal number of exceptional values of Gauss maps for various classes of surfaces
• On the number of exceptional values of the Gauss map of minimal surfaces
• An estimate for the Gauss curvature of minimal surfaces in \(\mathbf R^m\) whose Gauss map omits a set of hyperplanes
• Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
• Modified defect relations for the Gauss map of minimal surfaces. II
• On the theory of covering surfaces.
• Complex Analytic Mappings of Riemann Surfaces I
• The Hyperbolicity of the Complement of 2n + 1 Hyperplanes in General Position in P n , and Related Results
• Modified defect relations for the gauss map of minimal surfaces, III
• On the Gauss map of minimal surfaces immersed in \(R^ n\)
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Curvature estimate on an open Riemann surface with the induced metric