On a fourth order equation in 3-D

Xingwang Xu; Paul C. Yang

doi:10.1051/cocv:2002023

On a fourth order equation in 3-D

Xingwang Xu
, Paul C. Yang

Mathematics

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

14 Scopus citations

Abstract

In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

Original language	English (US)
Pages (from-to)	1029-1042
Number of pages	14
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	8
DOIs	https://doi.org/10.1051/cocv:2002023
State	Published - Jun 2002

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Control and Optimization
Computational Mathematics

Keywords

Conformal invariance
Connected sum
Paneitz operator
Sobolev inequality

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10.1051/cocv:2002023

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title = "On a fourth order equation in 3-D",

abstract = "In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.",

keywords = "Conformal invariance, Connected sum, Paneitz operator, Sobolev inequality",

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

year = "2002",

month = jun,

doi = "10.1051/cocv:2002023",

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T1 - On a fourth order equation in 3-D

AU - Xu, Xingwang

AU - Yang, Paul C.

PY - 2002/6

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N2 - In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

AB - In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

KW - Conformal invariance

KW - Connected sum

KW - Paneitz operator

KW - Sobolev inequality

UR - https://www.scopus.com/pages/publications/4243085108

UR - https://www.scopus.com/pages/publications/4243085108#tab=citedBy

U2 - 10.1051/cocv:2002023

DO - 10.1051/cocv:2002023

M3 - Article

AN - SCOPUS:4243085108

SN - 1292-8119

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EP - 1042

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

ER -

On a fourth order equation in 3-D

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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