Chavel, Isaac; Feldman, Edgar A. Diffusion on manifolds with small handles. (English) Zbl 0574.58032 Indiana Univ. Math. J. 34, 449-461 (1985). The authors show that local topological perturbations of a Riemannian manifold M may only slightly influence the spectrum of the corresponding Laplace-Beltrami operator \(\Delta\). The proof is based on the result obtained in this paper that the Brownian motion on M ”hardly notice” a small tubular neighborhood of any compact submanifold of codimension larger than one. The research continues the authors’ previous study [see Comment. Math. Helv. 56, 83-102 (1981; Zbl 0473.53037); Math. Z. 184, 435-448 (1983; Zbl 0525.53054)]. Reviewer: Y.Kifer Cited in 1 Document MSC: 58J65 Diffusion processes and stochastic analysis on manifolds 58J35 Heat and other parabolic equation methods for PDEs on manifolds Keywords:diffusion; Riemannian manifold; spectrum; Laplace-Beltrami operator Citations:Zbl 0473.53037; Zbl 0525.53054 PDFBibTeX XMLCite \textit{I. Chavel} and \textit{E. A. Feldman}, Indiana Univ. Math. J. 34, 449--461 (1985; Zbl 0574.58032) Full Text: DOI