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- Title
First eigenvalue of the Laplacian on compact surfaces for large genera.
- Authors
Ros, Antonio
- Abstract
For any Riemannian metric d s 2 on a compact surface of genus g, Yang and Yau proved that the normalized first eigenvalue of the Laplacian λ 1 (d s 2) A r e a (d s 2) is bounded in terms of the genus. In particular, if Λ 1 (g) is the supremum for each g, it follows that the asymptotic growth of the sequence Λ 1 (g) is no larger than the one of 4 π g . Recently Ros, for g = 3 , and Karpukhin and Vinokurov, for the general case, improve these bounds. In this paper we obtain a sharper result for Λ 1 (g) and we show that lim sup g → ∞ 1 g Λ 1 (g) ≤ 4 (3 - 5) π ≈ 3.056 π. <graphic href="209_2023_3382_Article_Equ26.gif"></graphic>
- Subjects
EIGENVALUES; RIEMANNIAN metric; LAPLACIAN matrices; RIEMANN surfaces
- Publication
Mathematische Zeitschrift, 2023, Vol 305, Issue 4, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-023-03382-8