Communications in Analysis and Geometry

Volume 29 (2021)

Number 2

Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity

Pages: 363 – 407

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n2.a4

Authors

Shengbing Deng (School of Mathematics and Statistics, Southwest University, Chongqing, China)

Seunghyeok Kim (Department of Mathematics and Research Institute for Natural Sciences, Hanyang University, Seoul, South Korea)

Angela Pistoia (Dipartimento SBAI, Universtá di Roma “La Sapienza”, Roma, Italy)

Abstract

Given an asymptotically hyperbolic manifold with minimal conformal infinity, we construct blowing-up solutions for linear perturbations of the fractional Yamabe problem on the conformal infinity provided that either the trace-free part of the second fundamental form or the covariant normal derivative of the normal component of the Ricci tensor on the conformal infinity is non-trivial.

Shengbing Deng has been partially supported financially by NSFC (No. 11971392) and Fundamental Research Funds for the Central Universities XDJK2019TY001. Seunghyeok Kim was partially supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF2017R1C1B507 6384). Angela Pistoia was partially supported by Sapienza University of Roma Research Project Sistemi ellittici non lineari e applicazioni.

Received 15 June 2017

Accepted 6 July 2018