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.
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