@article{7bb2e9665c3a491b940ef7a1321cf76b,

title = "On compact 3-manifolds with nonnegative scalar curvature with a CMC boundary component",

abstract = "We apply the Riemannian Penrose inequality and the Riemannian positive mass theorem to derive inequalities on the boundary of a class of compact Riemannian 3-manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e., a 2-sphere with positive constant mean curvature; and the rest of the boundary, if nonempty, consists of closed minimal surfaces. A key step in our proof is the construction of a collar extension that is inspired by the method of Mantoulidis-Schoen.",

keywords = "CMC surfaces, Riemannian penrose inequality, Scalar curvature",

author = "Pengzi Miao and Naqing Xie",

note = "Funding Information: Received by the editors January 30, 2017. 2010 Mathematics Subject Classification. Primary 53C20; Secondary 83C99. Key words and phrases. Scalar curvature, CMC surfaces, Riemannian Penrose inequality. The first named author{\textquoteright}s research was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105. The second named author{\textquoteright}s research was partially supported by the National Science Foundation of China #11671089, #11421061. Funding Information: The first named author{\textquoteright}s research was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105. The second named author{\textquoteright}s research was partially supported by the National Science Foundation of China #11671089, #11421061. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

doi = "10.1090/tran/7500",

language = "English (US)",

volume = "370",

pages = "5887--5906",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "8",

}