Related papers: Divergent CR-Equivalences and Meromorphic Differen…
We introduce new invariant tensors in CR structures which can be viewed as higher order Levi forms. Using the second and third order tensors, we give a complete formal normal form (in the sense of Chern-Moser) for a real hypersurface at a…
There are solved standard problems related to Formal (Holomorphic) Segre preserving Mappings of non-trivial Real-Formal Hypersurfaces in $\mathbb{C}^{2}$.
We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained by suspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficient condition to obtain a normal form as a…
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…
We consider a smooth CR mapping $f$ from a real-analytic generic submanifold $M$ in $\bC^N$ into $\bC^N$. For $M$ of finite type and essentially finite at a point $p\in M$, and $f$ formally finite at $p$, we give a necessary and sufficient…
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature…
We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbb{C}^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e.…
The aim of this article is twofold: First we study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point…
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the {\em mapping locus} $E$ of (germs of nondegenerate) holomorphic maps $H \colon (M,p) \to M'$ between generic…
Local CR-generic submanifolds of C^N are in one-to-one correspondence with their respective graphing functions, but it is well known that (despite their importance) the Cartan-Hachtroudi-Chern-Moser invariants and coframes for Levi…
Let $\Omega \subset {\mathbb C}^n \times {\mathbb R}$ be a bounded domain with smooth boundary such that $\partial \Omega$ has only nondegenerate elliptic CR singularities, and let $f \colon \partial \Omega \to {\mathbb C}$ be a smooth…
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…
Searching normal forms for real analytic submanifolds of C^n involves convergence problems. In 1983, J.K. Moser and S.M. Webster provided examples of real analytic surfaces in C^2 having an isolated hyperbolic (in the sense of E. Bishop)…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…
It is proved that dicritical singularities of real analytic Levi-flat sets coincide with the set of Segre degenerate points.
We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented pseudohermitian structures $\mathcal{P}_{+}$. We show that the functionals are continuous…
Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.