Mapping properties of the Laplacian in Sobolev spaces of forms on complete hyperbolic manifolds

被引：3

作者：

Bruna, J ^{[1
]}

Girbau, J ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2004年 / 25卷 / 02期

关键词：

Hodge-de Rham laplacian; rough Laplacian; Sobolev spaces; Riesz transforms; hyperbolic manifolds;

D O I：

10.1023/B:AGAG.0000018554.31037.23

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a complete manifold M with constant negative curvature, we prove that the rough Laplacian Delta(R) defines topological isomorphisms in the scale of Sobolev spaces H-p(s)(M) of p-forms for all p, 0 < p < n. For the de Rham Laplacian Delta and M = H-n, the Poincare hyperbolic space, this is shown too for 0 less than or equal to p less than or equal to n, p not equal n/2, p not equal (n +/- 1)/2.

引用

页码：151 / 176

页数：26

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