Prescription du spectre de Steklov dans une classe conforme

Abstract

On any compact manifold of dimension $n\ge 3$ with boundary, we prescibe any finite part of the Steklov spectrum whithin a given conformal class. In particular, we prescribe the multiplicity of the first eigenvalues. On a compact surface with boundary, we show that the multiplicity of the $k$-th eigenvalue is bounded independently of the metric. On the disk, we give more precise results : the multiplicity of the first and second positive eigenvalues are at most 2 and 3 respectively. For the Steklov-Neumann problem on the disk, we prove that the multiplicity of the $k$-th positive eigenvalue is at most $k+1$.

27pages, in French, 1 figure

Cited by in corpus (6)

• Sharp eigenvalue bounds and minimal surfaces in the ball
• Maximal metrics for the first Steklov eigenvalue on surfaces
• Multiplicité du spectre de Steklov sur les surfaces et nombre chromatique
• Conformal optimization of eigenvalues on surfaces with symmetries
• Robin and Steklov isospectral manifolds
• Heat invariants of the Steklov problem