Related papers: CR Paneitz operator and embeddability

For an $n$-dimensional compact submanifold $M^n$ in the Euclidean space $\mathbf R^{N}$, we study estimates for eigenvalues of the Paneitz operator on $M^n$. Our estimates for eigenvalues are sharp.

In this paper we prove new embedding results for compactly supported deformations of $CR$ submanifolds of $\mathbb{C}^{n+d}$: We show that if $M$ is a $2$-pseudoconcave $CR$ submanifold of type $(n,d)$ in $\mathbb{C}^{n+d}$, then any…

Let M be a smooth CR manifold of CR dimension n and CR codimension k, which is not compact, but has the local extension property E. We introduce the notion of "elementary pseudoconcavity" for M, which extends to CR manifolds the concept of…

We extend the notions of CR GJMS operators and Q-curvature to the case of partially integrable CR structures. The total integral of the CR Q-curvature turns out to be a global invariant of compact nondegenerate partially integrable CR…

Let $M$ be the image of a smooth CR embedding of a strictly pseudoconvex CR real hypersurface into a sphere. If the CR second fundamental form of $M$ vanishes, we show that $M$ is a totally geodesic submanifold.

The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…

This paper is a continuation of our paper [Med. J. Math 19, Article number: 31 (2022)] in which we extended the notion of generalized Drazin-Riesz invertible operators to closed operators. We establish here, results relating the notion of…

This note is aimed at simplifying current literature about compactness estimates for the Kohn-Laplacian on CR manifolds. The approach consists in a tangential basic estimate in the formulation given by the first author in \cite{Kh10} which…

The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a potential theoretic condition on $(0,q)$-forms that generalizes Catlin's property (P_q) to CR…

Let M be an orbit of a real semisimple Lie group G_0 acting on a complex a flag manifolds G/Q of its complexification G. We study the space of global CR functions on M and characterize those M which are strictly locally CR separable, i.e.…

Embedding discrete Markov chains into continuous ones is a famous open problem in probability theory with many applications. Inspired by recent progress, we study the closely related questions of embeddability of real and positive operators…

We endeavour a systematic approach for the removal of singularities for CR functions on an arbitrary embeddable CR manifold.

This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is ''optimal''…

Let $X$ be a complex manifold and $M\subset X$ a compact, smooth, pseudoconvex CR manifold of dimension $2n-1$. (Here $n\ge 3$ or, in case $n=2$, it is made the extra assumption that $\dib_b$ has closed range on functions.) Assume that…

A pseudo-Einstein contact form plays a crucial role in defining some global invariants of closed strictly pseudoconvex CR manifolds. In this paper, we prove that the existence of a pseudo-Einstein contact form is preserved under…

The purpose of this article is to study Lipschitz CR mappings from an $h$-extendible (or semi-regular) hypersurface in $\mbb C^n$. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A…

We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a…

We relate a recently introduced non-local geometric invariant of compact strictly pseudoconvex Cauchy-Riemann (CR) manifolds of dimension 3 to various eta-invariants in CR geometry: on the one hand a renormalized eta-invariant appearing…

We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant energy functional for the Paneitz operator on a compact Riemannian manifold with…

We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.