Minimal Surfaces through Nevanlinna Theory

Min Ru

Published by De Gruyter 2023

Minimal Surfaces through Nevanlinna Theory

Min Ru

Volume 92 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110989557

Overview
Contents

About this book

The study of minimal surfaces is an important subject in differential geometry, and Nevanlinna theory is an important subject in complex analysis and complex geometry. This book discusses the interaction between these two subjects. In particular, it describes the study of the value distribution properties of the Gauss map of minimal surfaces through Nevanlinna theory, a project initiated by the prominent differential geometers Shiing-Shen Chern and Robert Osserman.

Presents the basis theory of minimal surfaces.
Develops the classical theory of holomorphic curves in the projective space with Ahlfors' approach
Examines the y the value distribution properties for the Gauss maps of the immersed harmonic surfaces.

Author / Editor information

Min Ru, University of Houston, U.S.A.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
1 Some background in differential geometry Requires Authentication Unlicensed Licensed Download PDF	1
2 Analysis and geometry of complex functions Requires Authentication Unlicensed Licensed Download PDF	19
3 Minimal surfaces in R³ Requires Authentication Unlicensed Licensed Download PDF	47
4 The Nevanlinna theory Requires Authentication Unlicensed Licensed Download PDF	74
5 Gauss maps of minimal surfaces in R^m Requires Authentication Unlicensed Licensed Download PDF	135
6 Nevanlinna theory on the open ball B(R⁰) ⊂ Cⁿ and the nonintegrated defect relation Requires Authentication Unlicensed Licensed Download PDF	160
Bibliography Requires Authentication Unlicensed Licensed Download PDF	189
Index Requires Authentication Unlicensed Licensed Download PDF	193

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in complex analysis, number theory and complex geometry
Pages
- Front matter: 10
- Main content: 196
Illustrations
- Illustrations: 2
Keywords: Nevanlinna Theory; Minimal Spaces; Gauss Maps; Theory of Holomorphic Curves.

eBook

Published: May 8, 2023
ISBN: 9783110989557

Hardcover

Published: May 8, 2023
ISBN: 9783110999822