Small eigenvalues of the conformal Laplacian
نویسندگان
چکیده
منابع مشابه
Small Eigenvalues of the Conformal Laplacian
We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the α-genus.
متن کاملEigenvalues of the Conformal Laplacian
We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the α-genus.
متن کاملExtremal eigenvalues of the Laplacian in a conformal class of metrics : the ” conformal spectrum ”
Let M be a compact connected manifold of dimension n endowed with a conformal class C of Riemannian metrics of volume one. For any integer k ≥ 0, we consider the conformal invariant λk(C) defined as the supremum of the k-th eigenvalue λk(g) of the Laplace-Beltrami operator ∆g, where g runs over C. First, we give a sharp universal lower bound for λk(C) extending to all k a result obtained by Fri...
متن کاملEigenvalues of the normalized Laplacian
A graph can be associated with a matrix in several ways. For instance, by associating the vertices of the graph to the rows/columns and then using 1 to indicate an edge and 0 otherwise we get the adjacency matrix A. The combinatorial Laplacian matrix is defined by L = D − A where D is a diagonal matrix with diagonal entries the degrees and A is again the adjacency matrix. Both of these matrices...
متن کاملEigenvalues of the Laplacian acting on p - forms and metric conformal deformations
Let (M,g) be a compact connected orientable Riemannian manifold of dimension n ≥ 4 and let λk,p(g) be the k-th positive eigenvalue of the Laplacian ∆g,p = dd +dd acting on differential forms of degree p on M . We prove that the metric g can be conformally deformed to a metric g, having the same volume as g, with arbitrarily large λ1,p(g ) for all p ∈ [2, n − 2]. Note that for the other values o...
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: Geometric And Functional Analysis
سال: 2003
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-003-0419-6