On the essential spectrum of complete non-compact manifolds
نویسندگان
چکیده
منابع مشابه
On the essential spectrum of complete non-compact manifolds
In this paper, we prove that the Lp essential spectra of the Laplacian on functions are [0,+∞) on a noncompact complete Riemannian manifold with non-negative Ricci curvature at infinity. The similar method applies to gradient shrinking Ricci soliton, which is similar to non-compact manifold with non-negative Ricci curvature in many ways. © 2010 Elsevier Inc. All rights reserved.
متن کاملSome Properties of Non-compact Complete Riemannian Manifolds
In this paper, we study the volume growth property of a non-compact complete Riemannian manifold X . We improve the volume growth theorem of Calabi (1975) and Yau (1976), Cheeger, Gromov and Taylor (1982). Then we use our new result to study gradient Ricci solitons. We also show that on X , for any q ∈ (0,∞), every non-negative L subharmonic function is constant under a natural decay condition ...
متن کاملThe Monge problem on non-compact manifolds
In this paper we prove the existence of an optimal transport map on non-compact manifolds for a large class of cost functions that includes the case c(x, y) = d(x, y), under the only hypothesis that the source measure is absolutely continuous with respect to the volume measure. In particular, we assume compactness neither of the support of the source measure nor of that of the target measure.
متن کاملThe Spectrum of Twisted Dirac Operators on Compact Flat Manifolds
Let M be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of M , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group Z2 , we give a very simple expression for the multiplicities of eigenvalues that allows t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2011
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2010.10.010