Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations

TL;DR

This paper investigates the asymptotic behavior of Palais-Smale sequences for fractional Yamabe equations on hyperbolic manifolds, showing they decompose into solutions plus bubbles, with non-interference among multiple bubbles.

Contribution

It provides a detailed decomposition of Palais-Smale sequences into solutions and bubbles, extending understanding of fractional Yamabe equations on hyperbolic manifolds.

Findings

Palais-Smale sequences decompose into solutions and bubbles

Finite number of bubbles correspond to rescaled fundamental solutions

Multi-bubbles do not interfere with each other

Abstract

In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solutions to the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.