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ABSTRACT AND CLASSICAL HODGE-DE RHAM THEORY.
- Source :
- Analysis & Applications; Jan2012, Vol. 10 Issue 1, p91-111, 21p
- Publication Year :
- 2012
-
Abstract
- In previous work, with Bartholdi and Schick [1], the authors developed a Hodge-de Rham theory for compact metric spaces, which defined a cohomology of the space at a scale α. Here, in the case of Riemannian manifolds at a small scale, we construct explicit chain maps between the de Rham complex of differential forms and the L<superscript>2</superscript> complex at scale α, which induce isomorphisms on cohomology. We also give estimates that show that on smooth functions, the Laplacian of [1], when appropriately scaled, is a good approximation of the classical Laplacian. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02195305
- Volume :
- 10
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 70251065
- Full Text :
- https://doi.org/10.1142/S0219530512500054