Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$

Nikolai Nadirashvili (1) , Yannick Sire (2)

1 I2M - Institut de Mathématiques de Marseille
2 JHU - Johns Hopkins University

We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on $\mathbb S^2$. Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.

Mots clés: isoperimetric inequality; Hersch’s inequality; Riemannian surfaces; the Laplace-Beltrami operator

Domaines: Géométrie différentielle [math.DG]

Nikolai Nadirashvili, Yannick Sire. Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$. 2016. ⟨hal-01338374⟩