@article{cb598bb5e84f4848a96ba24f908d49cf,

title = "A POSITIVE MASS THEOREM FOR MANIFOLDS WITH BOUNDARY",

abstract = "We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green{\textquoteright}s function. The theorem also holds if the conformal Green{\textquoteright}s function is replaced by the standard Green{\textquoteright}s function for the Laplacian operator. As an application, we obtain an inequality relating the mass and harmonic functions that generalizes H. Bray{\textquoteright}s mass-capacity inequality in his proof of the Riemannian Penrose conjecture.",

keywords = "positive mass theorem with boundary",

author = "Sven Hirsch and Pengzi Miao",

note = "Funding Information: This work was initiated when Hirsch was visiting the University of Miami (UM) in October 2018. He is grateful for the hospitality of the department of mathematics at UM. He also wants to thank H. Bray for many encouraging discussions and interest in this work. Miao's research is partially supported by Simons Foundation Collaboration Grant for Mathematicians #585168. Funding Information: This work was initiated when Hirsch was visiting the University of Miami (UM) in October 2018. He is grateful for the hospitality of the department of mathematics at UM. He also wants to thank H. Bray for many encouraging discussions and interest in this work. Miao{\textquoteright}s research is partially supported by Simons Foundation Collaboration Grant for Mathematicians #585168. Publisher Copyright: {\textcopyright} 2020",

year = "2020",

month = jun,

doi = "10.2140/pjm.2020.306.185",

language = "English (US)",

volume = "306",

pages = "185--201",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "1",

}