The Hölder-Poincaré duality for Lq,p-cohomology

Vladimir Gol'dshtein; Marc Troyanov

doi:10.1007/s10455-011-9269-x

The Hölder-Poincaré duality for L_q,p-cohomology

Vladimir Gol'dshtein, Marc Troyanov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove the following version of Poincaré duality for reduced L_q,p-cohomology: For any 1 < q, p < ∞, the L_q,p-cohomology of a Riemannian manifold is in duality with the interior L_p',q'-cohomology for 1/p + 1/p′ = 1/q + 1/q′ = 1.

Original language	English
Pages (from-to)	25-45
Number of pages	21
Journal	Annals of Global Analysis and Geometry
Volume	41
Issue number	1
DOIs	https://doi.org/10.1007/s10455-011-9269-x
State	Published - 1 Jan 2012

Keywords

Parabolicity
Poincaré duality

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

Access to Document

10.1007/s10455-011-9269-x

Cite this

@article{6068172c265a4a3bb8b247013bce736e,

title = "The H{\"o}lder-Poincar{\'e} duality for Lq,p-cohomology",

abstract = "We prove the following version of Poincar{\'e} duality for reduced Lq,p-cohomology: For any 1 < q, p < ∞, the Lq,p-cohomology of a Riemannian manifold is in duality with the interior Lp',q'-cohomology for 1/p + 1/p′ = 1/q + 1/q′ = 1.",

keywords = "Parabolicity, Poincar{\'e} duality",

author = "Vladimir Gol'dshtein and Marc Troyanov",

note = "Funding Information: This study was partially supported by Israel Scientific Foundation (Grant no. 1033/07).",

year = "2012",

month = jan,

day = "1",

doi = "10.1007/s10455-011-9269-x",

language = "English",

volume = "41",

pages = "25--45",

journal = "Annals of Global Analysis and Geometry",

issn = "0232-704X",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - The Hölder-Poincaré duality for Lq,p-cohomology

AU - Gol'dshtein, Vladimir

AU - Troyanov, Marc

N1 - Funding Information: This study was partially supported by Israel Scientific Foundation (Grant no. 1033/07).

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We prove the following version of Poincaré duality for reduced Lq,p-cohomology: For any 1 < q, p < ∞, the Lq,p-cohomology of a Riemannian manifold is in duality with the interior Lp',q'-cohomology for 1/p + 1/p′ = 1/q + 1/q′ = 1.

AB - We prove the following version of Poincaré duality for reduced Lq,p-cohomology: For any 1 < q, p < ∞, the Lq,p-cohomology of a Riemannian manifold is in duality with the interior Lp',q'-cohomology for 1/p + 1/p′ = 1/q + 1/q′ = 1.

KW - Parabolicity

KW - Poincaré duality

UR - https://www.scopus.com/pages/publications/81155137822

U2 - 10.1007/s10455-011-9269-x

DO - 10.1007/s10455-011-9269-x

M3 - Article

AN - SCOPUS:81155137822

SN - 0232-704X

VL - 41

SP - 25

EP - 45

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 1

ER -