The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3477–3490 | Cite as

Conformal CR Positive Mass Theorem

  • Pak Tung Ho


In this paper, we prove the following version of conformal CR positive mass theorem: Suppose that \((N, J,\theta )\) and \((N, J,\hat{\theta }=e^{2f}\theta )\) are three-dimensional asymptotically flat pseudohermitian manifolds such that their Tanaka-Webster curvatures satisfy \(e^{2f}\hat{R}-R\ge 0.\) Then the p-mass of \((N, J, \theta )\) and \((N, J, \hat{\theta })\) satisfy \( m(J, \hat{\theta })-m(J, \theta )\ge 0, \) and equality holds if and only if \(\hat{\theta }=\theta \). We also prove that the p-mass is independent of the choice of the sequence of coordinates spheres.


Positive mass theorem CR manifold Conformal 

Mathematics Subject Classification

Primary 32V20 Secondary 35R01 53A30 53C17 



The author would like to thank Prof. Paul Yang for the discussions, guidance, and encouragements which lead to this work. The author is grateful to Princeton University for the kind hospitality, and he was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MEST) (No.201731033.01).


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Authors and Affiliations

  1. 1.Department of MathematicsSogang UniversitySeoulKorea

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