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A positive mass theorem in three dimensional Cauchy-Riemann geometry

Author(s): Cheng, Jih-Hsin; Malchiodi, Andrea; Yang, Paul C

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dc.contributor.authorCheng, Jih-Hsin-
dc.contributor.authorMalchiodi, Andrea-
dc.contributor.authorYang, Paul C-
dc.date.accessioned2019-08-29T17:02:06Z-
dc.date.available2019-08-29T17:02:06Z-
dc.date.issued2017-02-21en_US
dc.identifier.citationCheng, Jih-Hsin, Malchiodi, Andrea, Yang, Paul. (2017). A positive mass theorem in three dimensional Cauchy-Riemann geometry. ADVANCES IN MATHEMATICS, 308 (276 - 347. doi:10.1016/j.aim.2016.12.012en_US
dc.identifier.issn0001-8708-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1km8q-
dc.description.abstractWe define an ADM-like mass, called p-mass, for an asymptotically flat pseudohermitian manifold. The p-mass for the blow-up of a compact pseudohermitian manifold (with no boundary) is identified with the first nontrivial coefficient in the expansion of the Green function for the CR Laplacian. We deduce an integral formula for the p-mass, and we reduce its positivity to a solution of Kohn’s equation. We prove that the p-mass is non-negative for (blow-ups of) compact 3-manifolds of positive CR Yamabe invariant and with non-negative CR Paneitz operator. Under these assumptions, we also characterize the zero mass case as the standard three dimensional CR sphere. We then show the existence of (non-embeddable) CR 3-manifolds having nonpositive Paneitz operator or negative p-mass through a second variation formula. Finally, we apply our main result to find solutions of the CR Yamabe problem with minimal energy. (C) 2016 Elsevier Inc. All rights reserved.en_US
dc.format.extent276 - 347en_US
dc.languageEnglishen_US
dc.language.isoen_USen_US
dc.relation.ispartofADVANCES IN MATHEMATICSen_US
dc.rightsAuthor's manuscripten_US
dc.titleA positive mass theorem in three dimensional Cauchy-Riemann geometryen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1016/j.aim.2016.12.012-
dc.date.eissued2017-01-02en_US
dc.identifier.eissn1090-2082-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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