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- W2199148757 abstract "Abstract We prove that on any compact manifold $M^{n}$ with boundary, there exists a conformal class $C$ such that for any Riemannian metric $gin C$ of unit volume, the first positive eigenvalue of the Neumann Laplacian satisfies ${itlambda}_{1}(M^{n},g)<n,text{Vol}(S^{n},g_{text{can}})^{2/n}$ . We also prove a similar inequality for the first positive Steklov eigenvalue. The proof relies on a handle decomposition of the manifold. We also prove that the conformal volume of $(M,C)$ is $text{Vol}(S^{n},g_{text{can}})$ , and that the Friedlander–Nadirashvili invariant and the Möbius volume of $M$ are equal to those of the sphere. If $M$ is a domain in a space form, $C$ is the conformal class of the canonical metric." @default.
- W2199148757 created "2016-06-24" @default.
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- W2199148757 date "2014-10-28" @default.
- W2199148757 modified "2023-09-25" @default.
- W2199148757 title "Spectre et géométrie conforme des variétés compactes à bord" @default.
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- W2199148757 doi "https://doi.org/10.1112/s0010437x14007696" @default.
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