Singular Yamabe-type problems with an asymptotically flat metric

• Jiguang Bao ^[1] ; Yimei Li ^[2] ; Kun Wang ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
  2. [2] Beijing Jiaotong University

     Beijing Jiaotong University

     China

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 4, 2024, págs. 1351-1386
• Idioma: inglés
• DOI: 10.4171/RMI/1458
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we study the asymptotic symmetry and local behavior of positive solutions at infinity to the equation −L g u=∣x∣ τ u n−2n+2+2τ outside a bounded set in Rn , where n≥3, −2<τ<0, and Lg is the conformal Laplacian with asymptotically flat Riemannian metric g. We prove that the solution, at ∞, either converges to a fundamental solution of the Laplace operator on the Euclidean space, or is asymptotically close to a Fowler-type solution defined on Rn ∖{0}.