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 first eigenvalue of the Laplacian for plane domains

Author: Christopher B. Croke
Journal: Proc. Amer. Math. Soc. 81 (1981), 304-305
MSC: Primary 35P15; Secondary 52A40
MathSciNet review: 593476
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an improved lower bound for the first eigenvalue of the Laplacian of a connected plane domain in terms of its inradius and connectivity.

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

  • [1] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, A Symposium in Honor of S. Bochner, Princeton Univ. Press, Princeton, N. J., 1970, pp. 195-199. MR 0402831 (53:6645)
  • [2] S.-Y. Cheng, On the Hayman-Osserman-Taylor inequality (preprint).
  • [3] W. Hayman, Some bounds for principal frequency, Applicable Anal. 7 (1978), 247-254. MR 0492339 (58:11468)
  • [4] R. Osserman, A note on Hayman's theorem on the bass note of a drum, Comment. Math. Helv. 52 (1977), 545-555. MR 0459099 (56:17297)
  • [5] L. A. Santaló, Sobre el circulo de radio maximo contenido en un recinto, Rev. Un. Mat. Argentina 10 (1945), 155-167.
  • [6] M. Taylor, Estimate on the fundamental frequency of a drum, Duke Math. J. 46 (1979), 447-453. MR 534061 (81g:35097)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P15, 52A40

Retrieve articles in all journals with MSC: 35P15, 52A40

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society