Session S33 - Spectral Geometry

Monday, July 12, 14:00 ~ 14:20 UTC-3

On the spectrum of the Laplace operator of rank one symmetric spaces

Paolo Piccione

Universidade de S\~ao Paulo, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will discuss the computation of the first eigenvalue of the Laplace operator of a homogeneous compact rank one symmetric space (CROSS), and give two applications of such computation. The first application is a proof that that isospectral CROSSes are isometric. The second application concerns the stability of the homogeneous metrics as solutions of the Yamabe problem. If time allows, I will also present a description of the full Laplace spectrrum of distance spheres in symmetric spaces of rank one, with applications to a bifurcation problem for CMC hypersurfaces.

Joint work with R. Bettiol (CUNY, Lehman College, USA) and E. Lauret (Univ. Nacional del Sur, Argentina).

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