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EnglishWe 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 G reen function for the CR Laplacian. We deduce an integral formula for the p-mass, and we reduce its po sitivity 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 Tanaka-Webster class and with non-negative CR Paneitz operator . Under these assumptions, we also characterize the zero mass case as the standard three dimension al CR sphere. We then show the existence of (non-embeddable) CR 3-manifolds having nonpositive Paneitz ope rator or negative p-mass through a second variation formula. Finally, we apply our main result to find solut ions of the CR Yamabe problem with minimal energy
| Titolo: | A positive mass theorem in three dimensional Cauchy-Riemann geometry | |
| Autori: | ||
| Data di pubblicazione: | 2017 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aim.2016.12.012 | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Parole Chiave: | CR geometry, positive mass theorem, conformal geometry, Tanaka-Webster Yamabe problem | |
| Handle: | http://hdl.handle.net/1234/56329 http://hdl.handle.net/11384/56329 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| CMY-AIM.pdf | CMY-AIM | Published version | Non pubblico | Administrator Richiedi una copia |
| CMY-AIM-PP.pdf | CMY-AIM-PP | Accepted version (post-print) |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11384/56329
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