کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9495457 1335128 2005 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Lp independence of the spectrum of the Hodge Laplacian on non-compact manifolds
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the Lp independence of the spectrum of the Hodge Laplacian on non-compact manifolds
چکیده انگلیسی
The central aim of this paper is the study of the spectrum of the Hodge Laplacian on differential forms of any order k in Lp. The underlying space is a C∞-smooth open manifold MN with Ricci Curvature bounded below and uniformly subexponential volume growth. It will be demonstrated that on such manifolds the Lp spectrum of the Hodge Laplacian on differential k-forms is independent of p for 1⩽p⩽∞, whenever the Weitzenböck Tensor on k-forms is also bounded below. It follows as a corollary that the isolated eigenvalues of finite multiplicity are Lp independent. The proof relies on the existence of a Gaussian upper bound for the Heat kernel of the Hodge Laplacian. By considering the Lp spectra on the Hyperbolic space HN+1 we conclude that the subexponential volume growth condition is necessary in the case of one-forms. As an application, we will show that the spectrum of the Laplacian on one-forms has no gaps on certain manifolds with a pole or that are in a warped product form. This will be done under less strict curvature restrictions than what has been known so far and it was achieved by finding the L1 spectrum of the Laplacian.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 224, Issue 1, 1 July 2005, Pages 22-48
نویسندگان
,