Essential spectrum of a class of Riemannian manifolds

2012/05/24 by Luiz Antônio C. Monte, Monte, Luiz Antonio C., J. Fábio Montenegro +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · doi:10.48550/arxiv.1205.5428

openalex publication_date 2012/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval. The results presented in this paper allow to determine the spectrum of the Laplace operator on unlimited regions of space forms, such as horoball in hyperbolic space and cones in Euclidean space.

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