Related papers: Extrinsic GJMS operators for submanifolds
Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…
We establish an algorithm which computes formulae for the CR GJMS operators, the $P^\prime$-operator, and the $Q^\prime$-curvature in terms of CR tractors. When applied to torsion-free pseudo-Einstein contact forms, this algorithm both…
Given a unitary representation of a Lie group $G$ on a Hilbert space $\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions of symmetric operators both using von Neumann's theorem and the theory of quadratic forms. We…
We completely resolve the boundary value problem for differential forms and conformally Einstein infinity in terms of the dual Hahn polynomials. Consequently, we produce explicit formulas for the Branson-Gover operators on Einstein…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…
We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product $H^{\ell} \times S^{d-\ell}$. We also…
We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$ acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars. We first…
In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the GJMS operators, which include the Yamabe and Paneitz operators. We give several…
On Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of…
This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…
We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation…
The Gaussian integral operator arises naturally as a local Euclidean approximation of the heat semigroup on a Riemannian manifold and plays a pivotal role in the analysis of graph Laplacians, particularly within the frameworks of manifold…
We compute explicit formulas for the curvature operators and Poincar\'e polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincar\'e polynomials using quantum numbers, giving a formula that mirrors the known…
We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…
In this paper, we mainly study the scattering operators for the Poincar\'{e}-Einstein manifolds. Those operators give the fractional GJMS operators $P_{2\gamma}$ for the conformal infinity. If a Poincar\'{e}-Einstein manifolds $(X^{n+1},…
We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on…