Minoration conforme du spectre du laplacien de Hodge-de Rham

Details Minoration conforme du spectre du laplacien de Hodge-de Rham Minoration conforme du spectre du laplacien de Hodge-de Rham

2006-04-27

arxiv.org/abs/math/0604591v1

manuscripta math, 123 (1), p. 15-23, 2007

Mathematics

Differential Geometry

11 pages, 2 figures, in french

Scientific paper

Let $M^n$ be a n-dimensional compact manifold, with $n\geq3$. For any conformal class C of riemannian metrics on M, we set $\mu_k^c(M,C)=\inf_{g\in C}\mu_{[\frac n2],k}(M,g)\Vol(M,g)^{\frac2n}$, where $\mu_{p,k}(M,g)$ is the k-th eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that $0<\mu_k^c(M,C)\leq\mu_k^c(S^n,[g_{can}])\leq k^{\frac2n}\mu_1^c(S^n,[g_{can}])$.

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