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Minoration conforme du spectre du laplacien de Hodge-de Rham

Pierre Jammes
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Abstract

Let $M^n$ be a n-dimensional compact manifold, with $n\geq3$. For any conformal class C of riemannian metrics on M, we set $μ_k^c(M,C)=\inf_{g\in C}μ_{[\frac n2],k}(M,g)\Vol(M,g)^{\frac2n}$, where $μ_{p,k}(M,g)$ is the k-th eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that $0<μ_k^c(M,C)\leqμ_k^c(S^n,[g_{can}])\leq k^{\frac2n}μ_1^c(S^n,[g_{can}])$.

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Pierre Jammes. 2006-04-27. Minoration conforme du spectre du laplacien de Hodge-de Rham. https://arxiv.org/abs/math/0604591

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