Extremal domains for the first eigenvalue of the Laplace-Beltrami operator. (English) Zbl 1166.53029
The main result of this paper is a proof for the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator for certain Riemannian metrics. The domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.
Reviewer: Radu Miron (Iaşi)
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
Keywords:
extremal domain; Laplace-Beltrami operator; first eigenvalue; scalar curvature; geodesic sphereReferences:
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