Minoration conforme du spectre du laplacien de Hodge-de Rham

• Autores: Pierre Jammes
• Localización: Manuscripta mathematica, ISSN 0025-2611, Vol. 123, Nº. 1, 2007, págs. 15-23
• Idioma: inglés
• DOI: 10.1007/s00229-007-0080-8
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• Resumen

  • Let M n be an n-dimensional compact manifold, with n = 3. For any conformal class C of riemannian metrics on M, we set , where µ p,k (M,g) is the kth eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that . We also prove that if g is a smooth metric such that , and n = 0,2,3 mod 4, then there is a non-zero corresponding eigenform of degree with constant length. As a corollary, on a four-manifold with non vanishing Euler characteristic, there is no such smooth extremal metric.