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期刊论文
Existence of the spectral gap for elliptic operators
Ark. Mat., 37 (1999), 395-407,-0001,():
Let M be a connected, noncompact, complete Riemannian manifold, consider the operator L=∆+∇V for some V ∈C2(M) with exp[V]integrable with respect to the Riemannian volume element. This paper studies the existence of the spectral gap of L. As a consequence of the main result, let be the distance function from a point o, then the spectral gap exists provided lim →∞ sup L<0 while the spectral gap does not existi fo is a pole and lim →∞ inf L≥0. Moreover, the elliptic operators on Rd are also studied.
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