@inbook{3c482f692d7b46ddbc9f9d15750a7651,

title = "Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics",

abstract = "We prove that conformal metrics on domains of the round sphere, with non-negative constant Q-curvature, and non-negative scalar curvature, has positive mean curvature on the boundary of embedded balls (in the round metric). As a result, such metrics have certain reflection symmetries if the complement of the domain is contained in a lower-dimensional round sphere. We also prove that the development map of a locally conformally flat metric with non-positive Schouten tensor is an embedding.",

keywords = "53C21, Conformal metrics, Primary 58J06, Q-curvature, Secondary 35B06, moving planes, moving spheres, σk-curvature",

author = "Chang, {Sun Yung A.} and Han, {Zheng Chao} and Paul Yang",

note = "Funding Information: Chang{\textquoteright}s work was partially supported by NSF through grant DMS-1509505. Part of Han{\textquoteright}s work was completed in summer 2015 when the author was on a visiting professorship appointment at North University of China. Yang{\textquoteright}s work was partially supported by NSF through grant DMS-1509505. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

doi = "10.1007/978-3-030-34953-0_3",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Birkhauser",

pages = "37--56",

booktitle = "Progress in Mathematics",

}