**CRM Monograph Series**

Volume: 20;
2003;
296 pp;
Hardcover

MSC: Primary 30;

Print ISBN: 978-0-8218-3357-5

Product Code: CRMM/20

List Price: $92.00

Individual Member Price: $73.60

**Electronic ISBN: 978-1-4704-3865-4
Product Code: CRMM/20.E**

List Price: $92.00

Individual Member Price: $73.60

#### Supplemental Materials

# Riemann Surfaces of Infinite Genus

Share this page
*Joel Feldman; Horst Knörrer; Eugene Trubowitz*

A co-publication of the AMS and Centre de Recherches Mathématiques

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
Kadomcev-Petviashvilli 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 co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in analysis and integrable systems.