Hardcover ISBN:  9780821833575 
Product Code:  CRMM/20 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470438654 
Product Code:  CRMM/20.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Hardcover ISBN:  9780821833575 
eBook: ISBN:  9781470438654 
Product Code:  CRMM/20.B 
List Price:  $225.00 $170.00 
MAA Member Price:  $202.50 $153.00 
AMS Member Price:  $180.00 $136.00 
Hardcover ISBN:  9780821833575 
Product Code:  CRMM/20 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470438654 
Product Code:  CRMM/20.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Hardcover ISBN:  9780821833575 
eBook ISBN:  9781470438654 
Product Code:  CRMM/20.B 
List Price:  $225.00 $170.00 
MAA Member Price:  $202.50 $153.00 
AMS Member Price:  $180.00 $136.00 

Book DetailsCRM Monograph SeriesVolume: 20; 2003; 296 ppMSC: Primary 30;
In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps.
The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of KadomcevPetviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces).
The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.
Titles in this series are copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and research mathematicians interested in analysis and integrable systems.

Table of Contents

Chapters

$L^2$cohomology, exhaustions with finite charge and theta series

The Torelli Theorem

Examples

The Kadomcev–Petviashvilli equation


Additional Material

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps.
The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of KadomcevPetviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces).
The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.
Titles in this series are copublished with the Centre de recherches mathématiques.
Graduate students and research mathematicians interested in analysis and integrable systems.

Chapters

$L^2$cohomology, exhaustions with finite charge and theta series

The Torelli Theorem

Examples

The Kadomcev–Petviashvilli equation