Conformal metrics in  R2m with constant Q-curvature and arbitrary volume

Xia Huang; Dong Ye

doi:10.1007/s00526-015-0907-1

Conformal metrics in R^2m with constant Q-curvature and arbitrary volume

Xia Huang
, Dong Ye^*

^*Corresponding author for this work

School of Mathematical Sciences

Université de Lorraine

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

12 Scopus citations

Abstract

We study the polyharmonic problem Δ^mu=±e^u in R^2m, with m≥2. In particular, we prove that for any V>0, there exist radial solutions of Δ^mu=-e^u such that (Formula Presented).It implies that for m odd, given any Q₀>0 and arbitrary volume V>0, there exist conformal metrics g on R^2m with constant Q-curvature equal to Q₀ and vol_(g) =V. This answers some open questions in Martinazzi’s work (Ann IHP Analyse non linéaire 30:969–982, 2013).

Original language	English
Pages (from-to)	3373-3384
Number of pages	12
Journal	Calculus of Variations and Partial Differential Equations
Volume	54
Issue number	4
DOIs	https://doi.org/10.1007/s00526-015-0907-1
State	Published - 1 Dec 2015

Keywords

35J30
35J91
53A30

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title = "Conformal metrics in R2m with constant Q-curvature and arbitrary volume",

abstract = "We study the polyharmonic problem Δmu=±eu in R2m, with m≥2. In particular, we prove that for any V>0, there exist radial solutions of Δmu=-eu such that (Formula Presented).It implies that for m odd, given any Q0>0 and arbitrary volume V>0, there exist conformal metrics g on R2m with constant Q-curvature equal to Q0 and vol(g) =V. This answers some open questions in Martinazzi{\textquoteright}s work (Ann IHP Analyse non lin{\'e}aire 30:969–982, 2013).",

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T1 - Conformal metrics in R2m with constant Q-curvature and arbitrary volume

AU - Huang, Xia

AU - Ye, Dong

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We study the polyharmonic problem Δmu=±eu in R2m, with m≥2. In particular, we prove that for any V>0, there exist radial solutions of Δmu=-eu such that (Formula Presented).It implies that for m odd, given any Q0>0 and arbitrary volume V>0, there exist conformal metrics g on R2m with constant Q-curvature equal to Q0 and vol(g) =V. This answers some open questions in Martinazzi’s work (Ann IHP Analyse non linéaire 30:969–982, 2013).

AB - We study the polyharmonic problem Δmu=±eu in R2m, with m≥2. In particular, we prove that for any V>0, there exist radial solutions of Δmu=-eu such that (Formula Presented).It implies that for m odd, given any Q0>0 and arbitrary volume V>0, there exist conformal metrics g on R2m with constant Q-curvature equal to Q0 and vol(g) =V. This answers some open questions in Martinazzi’s work (Ann IHP Analyse non linéaire 30:969–982, 2013).

KW - 35J30

KW - 35J91

KW - 53A30

UR - https://www.scopus.com/pages/publications/84947870684

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SN - 0944-2669

VL - 54

SP - 3373

EP - 3384

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

Conformal metrics in R^2m with constant Q-curvature and arbitrary volume

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