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On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups


Author: Emilio A. Lauret
Journal: Proc. Amer. Math. Soc. 148 (2020), 3375-3380
MSC (2010): Primary 35P15; Secondary 58C40, 53C30
DOI: https://doi.org/10.1090/proc/14969
Published electronically: March 4, 2020
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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.


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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
Email: emilio.lauret@uns.edu.ar

DOI: https://doi.org/10.1090/proc/14969
Keywords: Naturally reductive metric, Laplace eigenvalue, diameter, compact simple Lie group.
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
Article copyright: © Copyright 2020 American Mathematical Society