## Differential and Integral Equations

### Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature

Ali Hyder

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 32, Number 7/8 (2019), 423-454.

Dates
First available in Project Euclid: 2 May 2019

Hyder, Ali. Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature. Differential Integral Equations 32 (2019), no. 7/8, 423--454. https://projecteuclid.org/euclid.die/1556762424