On normal solvability of the exterior differentiation on a warped cylinder
type: Item
instance of: scholarly article
title: On normal solvability of the exterior differentiation on a warped cylinder
zbMATH Open document ID: 0844.58003
DOI: 10.1007/BF00971242
author: V. I. Kuz'minov
author: I. A. Shvedov
published in: Siberian Mathematical Journal
publication date: 1996-08-29T00:00:00Z
review text: The \(L_p\)-cohomology space \(H^k_p (M)\) of a manifold coincides with the reduced \(L_p\)-cohomology space \(\overline H^k_p (M)\) if and only if the exterior derivative \(d^{k - 1}_{p,M} : L^{k - 1}_p (M) \to L^k_p (M)\) is a normally solvable operator, i.e., it has a closed range. If \(\dim H^k_p (M) < \infty\) then \(d^{k - 1}_{p, M}\) is normally solvable. Due to J. Cheeger it is known that this holds for \(M\) obtained from a closed pseudomanifold by removing singularities. In the article under review the authors find necessary and sufficient normal solvability conditions for \(d^{k - 1}_{p, M}\) defined over a warped cylinder \(M = [a, b) \times_fY\). If \(\lim_{t \to b} f(t) = \infty\) then the normal solvability turns out to be equivalent to the validity of an embedding theorem for weighted Sobolev spaces on \([a,b)\).
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 58A14
zbMATH DE Number: 825536
zbMATH Keywords: \(L_ p\)-cohomology
zbMATH Keywords: exterior derivative
zbMATH Keywords: warped cylinder
reviewed by: Valery Borisovich Marenich
MaRDI profile type: Publication
cites work: Q3911109
cites work: Q4040202
full work available at URL: https://doi.org/10.1007/bf00971242
OpenAlex ID: W2015893132
description: scientific article; zbMATH DE number 825536