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2017 Conformally Euclidean metrics on $\mathbb R^n$ with arbitrary total $Q$-curvature
Ali Hyder
Anal. PDE 10(3): 635-652 (2017). DOI: 10.2140/apde.2017.10.635

Abstract

We study the existence of solution to the problem

(Δ)n2u = Qenu in n ,κ :=nQenudx < ,

where Q 0, κ(0,) and n 3. Using ODE techniques, Martinazzi (for n = 6) and Huang and Ye (for n = 4m + 2) proved the existence of a solution to the above problem with Q  constant > 0 and for every κ (0,). We extend these results in every dimension n 5, thus completely answering the problem opened by Martinazzi. Our approach also extends to the case in which Q is nonconstant, and under some decay assumptions on Q we can also treat the cases n = 3 and n = 4.

Citation

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Ali Hyder. "Conformally Euclidean metrics on $\mathbb R^n$ with arbitrary total $Q$-curvature." Anal. PDE 10 (3) 635 - 652, 2017. https://doi.org/10.2140/apde.2017.10.635

Information

Received: 5 August 2016; Revised: 8 November 2016; Accepted: 22 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1378.35327
MathSciNet: MR3641882
Digital Object Identifier: 10.2140/apde.2017.10.635

Subjects:
Primary: 35G20, 35R11, 53A30

Rights: Copyright © 2017 Mathematical Sciences Publishers

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