Related papers: Conformal harmonic forms, Branson-Gover operators …
In this paper, we address a classical case of the Calder\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\omega$ (with boundary $\gamma$) contained in a domain…
We show that conformal manifolds in $d\geq 3$ conformal field theories with at least 4 supercharges are K\"ahler-Hodge, thus extending to 3d ${\cal N}=2$ and 4d ${\cal N}=1$ similar results previously derived for 4d ${\cal N}=2$ and ${\cal…
The aim of this article is to construct a specific Poisson transform mapping differential forms on the sphere $S^{2n+1}$ endowed with its natural CR structure to forms on complex hyperbolic space. The transforms we construct have values…
An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…
Given a metric defined on a manifold of dimension three, we study the problem of finding a conformal filling by a Poincar\'e-Einstein metric on a manifold of dimension four. We establish a compactness result for classes of conformally…
Relativistic Quantum Mechanics suffers from structural problems which are traced back to the lack of a position operator $\hat{x}$, satisfying $[\hat{x},\hat{p}]=i\hbar\hat{1}$ with the ordinary momentum operator $\hat{p}$, in the basic…
In this paper we study upper and lower bounds of the index and the nullity for sequences of harmonic maps with uniformly bounded Dirichlet energy from a two-dimensional Riemann surface into a compact target manifold. The main difficulty…
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry…
The modular forms and weighted densities over the 1-dimensional manifold $M$ are transformed ``alike" under the group of linear fractional changes of coordinates, so the classifications of differential operators between spaces of (A)…
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…
We prove that a $4-$dimensional $C^2$ conformally compact Einstein manifold with H\"older continuous scalar curvature and with $C^{m,\alpha}$ boundary metric has a $C^{m,\alpha}$ compactification. We also study the regularity of the new…
We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of…
We study the renormalized volume of asymptotically hyperbolic Einstein (AHE in short) manifolds $(M,g)$ when the conformal boundary $\pl M$ has dimension $n$ even. Its definition depends on the choice of metric $h_0$ on $\partial M$ in the…
This work presents a novel class of metrics on a para-K\"{a}hler-Norden manifold $(M^{2m},F,g)$, derived from a conformal deformation of the Berger-type metric associated with the metric $g$. Initially, we examine the Levi-Civita link…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
We investigate on a Randall-Sundrum warped spacetime, a Kerr-like black hole in the conformal dilaton-Higgs $(\omega,\Phi)$ gravity model. We applied the antipodal boundary condition on the Klein surface using the $\mathds{Z}_2$-symmetry in…
The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from a breakdown of ISO(d,2) (with d=10 for D3…
The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Let $(M^4,g)$ be a closed Riemannian manifold of dimension four. We investigate the properties of metrics which are critical points of the eigenvalues of the Paneitz operator when considered as functionals on the space of Riemannian metrics…