English

A Remark On Case-Gursky-V\'etois identity and its applications

Differential Geometry 2024-10-15 v1 Analysis of PDEs

Abstract

Based on the works of Gursky (CMP, 1997), V\'etois (Potential Anal., 2023) and Case (Crelle's journal, 2024), we make use of an Obata type formula established in these works to obtain some Liouville type theorems on conformally Einstein manifolds. In particular, we solve Hang-Yang conjecture (IMRN, 2020) via an Obata-type argument and obtain optimal perturbation.

Keywords

Cite

@article{arxiv.2410.09393,
  title  = {A Remark On Case-Gursky-V\'etois identity and its applications},
  author = {Mingxiang Li and Juncheng Wei},
  journal= {arXiv preprint arXiv:2410.09393},
  year   = {2024}
}

Comments

15pages; comments are welcome