Positivity of Paneitz Operators

Xingwang Xu; Paul C. Yang

doi:10.3934/dcds.2001.7.329

Positivity of Paneitz Operators

Xingwang Xu, Paul C. Yang

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

20 Scopus citations

Abstract

In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.

Original language	English (US)
Pages (from-to)	329-342
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2001.7.329
State	Published - 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Keywords

Connected Sum
Eigenvalues
Paneitz Opertaor

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10.3934/dcds.2001.7.329

Cite this

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abstract = "In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.",

keywords = "Connected Sum, Eigenvalues, Paneitz Opertaor",

author = "Xingwang Xu and Yang, {Paul C.}",

year = "2001",

doi = "10.3934/dcds.2001.7.329",

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AU - Xu, Xingwang

AU - Yang, Paul C.

PY - 2001

Y1 - 2001

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AB - In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.

KW - Connected Sum

KW - Eigenvalues

KW - Paneitz Opertaor

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DO - 10.3934/dcds.2001.7.329

M3 - Article

AN - SCOPUS:0035632257

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VL - 7

SP - 329

EP - 342

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 2

ER -

Positivity of Paneitz Operators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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