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Minimal Surfaces through Nevanlinna Theory
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Min Ru
Language:
English
Published/Copyright:
2023
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
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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
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Frontmatter
I -
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Preface
VII -
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Contents
IX -
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1 Some background in differential geometry
1 -
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2 Analysis and geometry of complex functions
19 -
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3 Minimal surfaces in R3
47 -
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4 The Nevanlinna theory
74 -
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5 Gauss maps of minimal surfaces in Rm
135 -
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6 Nevanlinna theory on the open ball B(R0) ⊂ Cn and the nonintegrated defect relation
160 -
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Bibliography
189 -
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Index
193
Publishing information
Pages and Images/Illustrations in book
eBook published on:
May 8, 2023
eBook ISBN:
9783110989557
Hardcover published on:
May 8, 2023
Hardcover ISBN:
9783110999822
Pages and Images/Illustrations in book
Front matter:
10
Main content:
196
Illustrations:
2
Audience(s) for this book
Researchers and graduate students in complex analysis, number theory and complex geometry
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
