On CR Paneitz operators and CR pluriharmonic functions

@article{Hsiao2014OnCP,
  title={On CR Paneitz operators and CR pluriharmonic functions},
  author={Chin-Yu Hsiao},
  journal={Mathematische Annalen},
  year={2014},
  volume={362},
  pages={903-929}
}
  • Chin-Yu Hsiao
  • Published 1 May 2014
  • Mathematics
  • Mathematische Annalen
Let $$(X,T^{1,0}X)$$(X,T1,0X) be a compact orientable embeddable three dimensional strongly pseudoconvex CR manifold and let $$\mathrm{P}$$P be the associated CR Paneitz operator. In this paper, we show that (I) $${\mathrm{P}}$$P is self-adjoint and $$\mathrm{P}$$P has $$L^2$$L2 closed range. Let $$N$$N and $$\Pi $$Π be the associated partial inverse and the orthogonal projection onto $$\mathrm{Ker}\,\mathrm{P}$$KerP respectively, then $$N$$N and $$\Pi $$Π enjoy some regularity properties. (II… 

Prescribing the $\bar Q^{\prime}$-Curvature on Pseudo-Einstein CR 3-Manifolds

In this paper we study the problem of prescribing the $\bar Q^{\prime}$-curvature on pseudo-Einstein CR 3-manifolds. In the first stage we study the problem in the compact setting and we show that

Logarithmic Hardy-Littlewood-Sobolev Inequality on Pseudo-Einstein 3-manifolds and the Logarithmic Robin Mass

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,\theta)$, we study the existence of a contact structure conformal to $\theta$ for which the logarithmic Hardy-Littlewood-Sobolev

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds

The non-negativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this non-negativity for embeddable CR manifolds. This result and previous

CR geometry in 3-D

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

$\bar{Q}'$-curvature flow on Pseudo-Einstein CR manifolds

In this paper we consider the problem of prescribing the Q ′ -curvature on three dimensional Pseudo-Einstein CR manifolds. We study the gradient flow generated by the related functional and we will

Analysis of the critical CR GJMS operator

The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially

-curvature flow on Pseudo-Einstein CR manifolds

In this paper we consider the problem of prescribing the Q ′ -curvature on three dimensional Pseudo-Einstein CR manifolds. We study the gradient flow generated by the related functional and we will

References

SHOWING 1-10 OF 12 REFERENCES

The sharp lower bound for the first positive eigenvalue of the sublaplacian on a pseudohermitian 3-manifold

In this paper, we study a sharp lower bound of the first eigenvalue of the sublaplacian on a 3-dimensional pseudohermitian manifold with the CR Paneitz operator positive. In general cases, S.-Y. Li

Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants

Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the

EMBEDDED THREE-DIMENSIONAL CR MANIFOLDS AND THE NON-NEGATIVITY OF PANEITZ OPERATORS

Let ⊂ C 2 be a strictly pseudoconvex domain and M = @ be a smooth, compact and connected CR manifold embedded in C 2 with the CR structure induced from C 2 . The main result proved here is as

A Paneitz-type operator for CR pluriharmonic functions

We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and

Projections in several complex variables

This thesis consists two parts. In the first part, we completely study the heat equation method ofMenikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR

PSEUDO-EINSTEIN STRUCTURES ON CR MANIFOLDS

Etant donne une variete CR compacte non degeneree, on cherche une structure pseudohermitienne associee pour laquelle le tenseur de Ricci pseudohermitien est un multiple scalaire de la forme de Levi

The analysis of linear partial differential operators

the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certainproducts. Many products that you buy can be

Sur la singularité des noyaux de Bergman et de Szegö

© Journées Équations aux dérivées partielles, 1975, tous droits réservés. L’accès aux archives de la revue « Journées Équations aux dérivées partielles »