2016/09/20 by Toshiyuki Kobayashi, Kobayashi, Toshiyuki
Mathematics · #11F72 #22E40 #22E46 #53C35 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1609.05986
openalex publication_date 2016/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As is well-known for compact Riemann surfaces, eigenvalues of the Laplacianbare distributed discretely and most of eigenvalues vary viewed as functions on the Teichmuller space. We discuss a new feature in the Lorentzian geometry, or more generally, in pseudo-Riemannian geometry. One of the distinguished features is that L2-eigenvalues of the Laplacian may be distributed densely in R in pseudo-Riemannian geometry. For three-dimensional anti-de Sitter manifolds, we also explain another feature proved in joint with F. Kassel [Adv. Math. 2016] that there exist countably many L2-eigenvalues of the Laplacian that are stable under any small deformation of anti-de Sitter structure.