Harmonic forms on manifolds with edges

By Eugénie Hunsicker, Rafe Mazzeo. 2005

49 citations recorded by the source corpus.

Let (X, g) be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various polynomially weighted de Rham cohomology spaces of X, as well as the associated spaces of harmonic forms. In the unweighted case, this is closely related to recent work of Cheeger and Dai [5]. Because the metric g is incomplete, this requires a consideration of the various choices of ideal boundary conditions at the singular set. We also calculate the space of L2 harmonic forms for any complete edge metric on the regular part of X.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/62b8ecd0ecb92701bd32bc231f6fa41f203018c1

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks (2010, methodology): “” This procedure was used in other contexts by several authors [42, 61, 64, 63].”
Analytic Torsion on Manifolds with Edges (2011, methodology): “In order to simplify various calculations below, we write this operator using a rescaling of the form bundles, employed also by Brüning-Seeley [6] and in slightly different form in [17].”