Lower bounds for the first Dirichlet eigenvalue of the Laplacian for domains in hyperbolic space

DOI10.1017/S0305004115000626zbMath1371.58009MaRDI QIDQ5360368

Sergei Artamoshin

Publication date: 28 September 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (5)

New features of the first eigenvalue on negatively curved spaces ⋮ Uncertainty principle on 3-dimensional manifolds of constant curvature ⋮ Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds ⋮ Eigenvalues of the Laplacian on balls with spherically symmetric metrics ⋮ The vanishing of the fundamental gap of convex domains in \(\mathbb{H}^n\)

Cites Work

• On the lowest eigenvalue of the Hodge Laplacian on compact, negatively curved domains
• Eigenvalue comparison theorems and its geometric applications
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
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