Riemann surfaces of infinite genus / Joel Feldman, Horst Knörrer, Eugene Trubowitz.

Format:

Book

Author/Creator:

Feldman, Joel S., 1949-

Contributor:

Knörrer, Horst.

Trubowitz, Eugene.

Series:

CRM monograph series 1065-8599 ; v. 20.

CRM monograph series, 1065-8599 ; v. 20

Language:

English

Subjects (All):

Riemann surfaces.

Physical Description:

vii, 296 pages : illustrations ; 27 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2003]

Contents:

Chapter 1. L[superscript 2]-Cohomology, Exhaustions with Finite Charge and Theta Series 1

1. Square Integrable One Forms 3

2. Exhaustion Functions with Finite Charge 16

3. Parabolic Surfaces 25

4. Theta Functions 42

Chapter 2. The Torelli Theorem 63

5. Geometric Hypotheses 66

6. Pointwise Bounds on Differential Forms 79

7. Zeroes of the Theta Function 110

8. Riemann's Vanishing Theorem 124

9. The Geometry of the Theta Divisor 134

10. Hyperelliptic Theta Divisors 152

12. Hyperelliptic Surfaces 172

13. Heat Curves: Basic Properties 180

14. Heat Curves: Asymptotics 194

15. Heat Curves: Verification of the Geometric Hypotheses 216

16. Fermi Curves: Basic Properties 221

17. Fermi Curves: Asymptotics 223

18. Fermi Curves: Verification of the Geometric Hypotheses 240

B. A Quantitative Morse Lemma 245

Chapter 4. The Kadomcev-Petviashvilli Equation 249

19. The Formula for the Solution 250

20. Approximations 254

21. Real Periodic Potentials 277.

Notes:

Includes bibliographical references (pages 295-296).

ISBN:

082183357X

OCLC:

51817326