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July/August 2019 Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature
Ali Hyder
Differential Integral Equations 32(7/8): 423-454 (July/August 2019).

Abstract

In this article, we study the nonlocal equation $$ (-\Delta)^{\frac{n}{2}}u=(n-1)!e^{nu}\quad \text{in $\mathbb R$}, \quad\int_{\mathbb R}e^{nu}dx < \infty, $$ which arises in the conformal geometry. Inspired by the previous work of C.S. Lin and L. Martinazzi in even dimension and T. Jin, A. Maalaoui, L. Martinazzi, J. Xiong in dimension three, we classify all solutions to the above equation in terms of their behavior at infinity.

Citation

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Ali Hyder. "Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature." Differential Integral Equations 32 (7/8) 423 - 454, July/August 2019.

Information

Published: July/August 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07144913
MathSciNet: MR3945763

Subjects:
Primary: 35J30, 35R11, 53A30

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 7/8 • July/August 2019
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