Spectre et géométrie conforme des variétés compactes à bord

Content Provider	Scilit
Author	Jammes, Pierre
Copyright Year	2014
Description	Journal: Compositio Mathematica We prove that on any compact manifold $M^{n}$ with boundary, there exists a conformal class $C$ such that for any Riemannian metric $g\in C$ of unit volume, the first positive eigenvalue of the Neumann Laplacian satisfies ${\it\lambda}_{1}(M^{n},g). 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.
Ending Page	2126
Starting Page	2112
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x14007696
Journal	Compositio Mathematica
Issue Number	12
Volume Number	150
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2014-10-28
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory