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^*

^*此作品的通讯作者

数学科学学院

Université de Lorraine

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

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).

源语言	英语
页（从-至）	3373-3384
页数	12
期刊	Calculus of Variations and Partial Differential Equations
卷	54
期	4
DOI	https://doi.org/10.1007/s00526-015-0907-1
出版状态	已出版 - 1 12月 2015

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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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AU - Ye, Dong

PY - 2015/12/1

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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).

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

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

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