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

Nikolai Nadirashvili; Yannick Sire

arxiv: 1506.07017 · v5 · pith:E4LKFCZCnew · submitted 2015-06-23 · 🧮 math.DG

Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on mathbb S²

Nikolai Nadirashvili , Yannick Sire This is my paper

classification 🧮 math.DG

keywords eigenvalueinequalityisoperimetricmathbbthirdbuildsclassesconformal

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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.

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Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on mathbb S²

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