Argentina
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The first eigenvalue of a homogeneous CROSS
Fecha
2022-01-12Registro en:
Bettiol, Renato; Lauret, Emilio Agustin; Piccione, Paolo; The first eigenvalue of a homogeneous CROSS; Springer; The Journal Of Geometric Analysis; 32; 76; 12-1-2022; 1-53
1050-6926
CONICET Digital
CONICET
Autor
Bettiol, Renato
Lauret, Emilio Agustin
Piccione, Paolo
Resumen
We provide explicit formulae for the first eigenvalue of the Laplace--Beltrami operator on a compact rank one symmetric space (CROSS) endowed with any homogeneous metric. As consequences, we prove that homogeneous metrics on CROSSes are isospectral if and only if they are isometric, and also discuss their stability (or lack thereof) as solutions to the Yamabe problem.