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| CR Geometry in 3-D |
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Citation： |
Paul C. YANG.CR Geometry in 3-D[J].Chinese Annals of Mathematics B,2017,38(2):695~710 |
| Page view： 701
Net amount： 573 |
Authors： |
Paul C. YANG; |
Foundation： |
This work was supported by NSF grant DMS-1509505. |
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| Abstract： |
CR geometry studies the boundary of pseudo-convex manifolds. By
concentrating on a choice of a contact form, the local geometry
bears strong resemblence to conformal geometry. This paper deals
with the role conformally invariant operators such as the Paneitz
operator plays in the CR geometry in dimension three. While the sign
of this operator is important in the embedding problem, the kernel
of this operator is also closely connected with the stability of CR
structures. The positivity of the CR-mass under the natural sign
conditions of the Paneitz operator and the CR Yamabe operator is
discussed. The CR positive mass theorem has a consequence for the
existence of minimizer of the CR Yamabe problem. The pseudo-Einstein
condition studied by Lee has a natural analogue in this dimension,
and it is closely connected with the pluriharmonic functions. The
author discusses the introduction of new conformally covariant
operator $P$-prime and its associated $Q$-prime curvature and gives
another natural way to find a canonical contact form among the class
of pseudo-Einstein contact forms. Finally, an isoperimetric constant
determined by the $Q$-prime curvature integral is discussed. |
Keywords： |
Paneitz operator, Embedding problem, Yamabe equation, Mass,$P$-prime, $Q$-prime curvature |
Classification： |
58J05, 53C21 |
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