Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The length spectrum of a Riemann surface is always of unbounded multiplicity


Author: Burton Randol
Journal: Proc. Amer. Math. Soc. 78 (1980), 455-456
MSC: Primary 58G25; Secondary 30F10, 53C22
DOI: https://doi.org/10.1090/S0002-9939-1980-0553396-1
MathSciNet review: 553396
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: I show that the length spectrum of a Riemann surface is always of unbounded multiplicity, and indicate connections with recent work of Guillemin and Kazhdan.


References [Enhancements On Off] (What's this?)

  • [1] R. Abraham, Bumpy metrics, Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1970, pp. 1-3. MR 0271994 (42:6875)
  • [2] M. Dehn, Transformation der Kurven auf zweiseitigen Flächen, Math. Ann. 72 (1912), 413-421. MR 1511705
  • [3] M. Greendlinger, On Dehn's algorithms for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641-677. MR 0125020 (23:A2327)
  • [4] V. Guillemin and D. Kazhdan, Some inverse spectral results for negatively curved two-manifolds (preprint).
  • [5] R. Horowitz, Characters of free groups represented in the two-dimensional special linear group, Comm. Pure Appl. Math. 25 (1972), 635-649. MR 0314993 (47:3542)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G25, 30F10, 53C22

Retrieve articles in all journals with MSC: 58G25, 30F10, 53C22


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553396-1
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society