On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups
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Abstract:
Eldredge, Gordina, and Saloff-Coste recently conjectured that, for a given compact connected Lie group $G$, there is a positive real number $C$ such that $\lambda _1(G,g)\operatorname {diam}(G,g)^2\leq C$ for all left-invariant metrics $g$ on $G$. In this short note, we establish the conjecture for the small subclass of naturally reductive left-invariant metrics on a compact simple Lie group.References
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Additional Information
- Emilio A. Lauret
- Affiliation: Instituto de Matemática (INMABB), Departamento de Matemática, Universidad Nacional del Sur (UNS)-CONICET, Bahía Blanca, Argentina
- MR Author ID: 1016885
- ORCID: 0000-0003-3729-5300
- Email: emilio.lauret@uns.edu.ar
- Received by editor(s): May 29, 2019
- Received by editor(s) in revised form: November 15, 2019, and December 11, 2019
- Published electronically: March 4, 2020
- Additional Notes: This research was supported by grants from CONICET, FONCyT, SeCyT, and the Alexander von Humboldt Foundation (return fellowship)
- Communicated by: Guofang Wei
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3375-3380
- MSC (2010): Primary 35P15; Secondary 58C40, 53C30
- DOI: https://doi.org/10.1090/proc/14969
- MathSciNet review: 4108844