國立高雄大學圖資館 |

Language: English

Back

The geometric theory of complex variables

Record Type:	Electronic resources : Monograph/item
Title/Author:	The geometric theory of complex variablesby Peter V. Dovbush, Steven G. Krantz.
Author:	Dovbush, Peter V.
other author:	Krantz, Steven G.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 540 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Global analysis (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-031-77204-7
ISBN:	9783031772047$q(electronic bk.)

The geometric theory of complex variables
Dovbush, Peter V.

The geometric theory of complex variables[electronic resource] /by Peter V. Dovbush, Steven G. Krantz. - Cham :Springer Nature Switzerland :2025. - xi, 540 p. :ill., digital ;24 cm.

This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.

ISBN: 9783031772047$q(electronic bk.)

Standard No.: 10.1007/978-3-031-77204-7doiSubjects--Topical Terms:

199030
Global analysis (Mathematics)

LC Class. No.: QA614 / .D68 2025

Dewey Class. No.: 514.74

The geometric theory of complex variables
LDR:02210nmm a2200313 a 4500 001 680406
003 DE-He213
005 20250129115245.0
006 m d
007 cr nn 008maaau
008 251110s2025 sz s 0 eng d
020 $a 9783031772047$q(electronic bk.)
020 $a 9783031772030$q(paper)
024 7 $a 10.1007/978-3-031-77204-7 $2 doi
035 $a 978-3-031-77204-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614 $b .D68 2025
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 514.74 $2 23
090 $a QA614 $b .D743 2025
100 1 $a Dovbush, Peter V. $3 993133
245 1 4 $a The geometric theory of complex variables $h [electronic resource] / $c by Peter V. Dovbush, Steven G. Krantz.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xi, 540 p. : $b ill., digital ; $c 24 cm.
520 $a This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.
650 0 $a Global analysis (Mathematics) $3 199030
650 0 $a Manifolds (Mathematics) $3 198996
650 0 $a Functions of complex variables. $3 185972
650 0 $a Functional analysis. $3 200585
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Krantz, Steven G. $3 284340
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-77204-7
950 $a Mathematics and Statistics (SpringerNature-11649)