The CR Paneitz operator and the stability of CR pluriharmonic functions

Case, James F.; Chanillo, Sagun; Yang, Paul

doi:10.1016/j.aim.2015.10.002

Cited by 45 publications

(91 citation statements)

References 34 publications

(103 reference statements)

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“…We first recall the pseudo-Einstein condition for contact forms; we refer the reader to [23,9,16] for detail. A contact form θ is called pseudo-Einstein if the associated Tanaka-Webster connection satisfies (4.5)…”

Section: The Fefferman Metric and Chainsmentioning

confidence: 99%

Chains in CR geometry as geodesics of a Kropina metric

Cheng

Marugame

Matveev

et al. 2019

Advances in Mathematics

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With the help of a generalization of the Fermat principle in general relativity, we show that chains in CR geometry are geodesics of a certain Kropina metric constructed from the CR structure. We study the projective equivalence of Kropina metrics and show that if the kernel distributions of the corresponding 1-forms are non-integrable then two projectively equivalent metrics are trivially projectively equivalent. As an application, we show that sufficiently many chains determine the CR structure up to conjugacy, generalizing and reproving the main result of [10]. The correspondence between geodesics of the Kropina metric and chains allows us to use the methods of metric geometry and the calculus of variations to study chains. We use these methods to re-prove the result of [18] that locally any two points of a strictly pseudoconvex CR manifolds can be joined by a chain. Finally, we generalize this result to the global setting by showing that any two points of a connected compact strictly pseudoconvex CR manifold which admits a pseudo-Einstein contact form with positive Tanaka-Webster scalar curvature can be joined by a chain.

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Section: The Fefferman Metric and Chainsmentioning

confidence: 99%

Chains in CR geometry as geodesics of a Kropina metric

Cheng

Marugame

Matveev

et al. 2019

Advances in Mathematics

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“…In this case, Branson's Q-curvature (that corresponds to our case γ = m, see (4.1)), vanishes identically and thus it is not an interesting object when restricting to pluriharmonics. Recently, [44] (see also [12]) has constructed new GJMS operators P ′ k using the original [37] ambient metric construction. It would be interesting to see those from the scattering and extension point of view.…”

Section: Equality Is Attained If and Only Ifmentioning

confidence: 99%

An extension problem for the CR fractional Laplacian

Frank

González

Monticelli

et al. 2015

Advances in Mathematics

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“…The research of the author is partially supported by NSF grant DMS-1509505. 1 As proved by Beckner [Bec93] and Chang-Yang [CY13], the pair (P g , Q g ) also apperas in the Moser-Trudinger inequality for higher order operators.…”

Section: Introductionmentioning

confidence: 89%

On the Sobolev–Poincaré Inequality of CR-manifolds

Wang

Yang

2018

International Mathematics Research Notices

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The purpose is to study the CR-manifold with a contact structure conformal to the Heisenberg group. In our previous work [WY17], we have proved that if the Q ′ -curvature is nonnegative, and the integral of Q ′ -curvature is below the dimensional bound c ′ 1 , then we have the isoperimetric inequality. In this paper, we manage to drop the condition on the nonnegativity of the Q ′ -curvature. We prove that the volume form e 4u is a strong A ∞ weight. As a corollary, we prove the Sobolev-Poincaré inequality on a class of CR-manifolds with integrable Q ′ -curvature.

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The CR Paneitz operator and the stability of CR pluriharmonic functions

Cited by 45 publications

References 34 publications

Chains in CR geometry as geodesics of a Kropina metric

Chains in CR geometry as geodesics of a Kropina metric

An extension problem for the CR fractional Laplacian

On the Sobolev–Poincaré Inequality of CR-manifolds

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