Related papers: Pavlovic's theorem in space
We prove that, given a planar bi-Lipschitz homeomorphism $u$ defined on the boundary of the unit square, it is possible to extend it to a function $v$ of the whole square, in such a way that $v$ is still bi-Lipschitz. In particular,…
We generalize the Ruh-Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.
For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We prove a Lefschetz-type coincidence theorem: if the Lefschetz…
It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…
In this paper, we investigate some properties on harmonic functions and solutions to Poisson equations. First, we will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma for harmonic…
We completely characterize the left-symmetric points, the right-symmetric points, and, the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric)…
This paper introduces the classically successful theory of Toeplitz operators on the Hardy space over the unit disk to a new domain in $\mathbb C^d$ -- the symmetrized polydisk.
We continue our study [Ou4] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian…
A classical result in the theory of Hopf algebras concerns the uniqueness and existence of integrals: for an arbitrary Hopf algebra, the integral space has dimension $\leq 1$, and for a finite dimensional Hopf algebra, this dimension is…
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.
We prove a version of Poincar\'e's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can…
We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in $\mathbb{R}^n$, for $n\geq 2$, called bounded integrable parameterization mappings, or BIP maps for short. These…
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference…
The classical Besicovitch-Federer projection theorem implies that the d-dimensional Hausdorff measure of a set in Euclidean space with non-negligible d-unrectifiable part will strictly decrease under orthogonal projection onto almost every…
A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
We survey several methods of extending quasisymmetric homeomorphisms of the real line to bi-Lipschitz diffeomorphisms of the upper half-plane with respect to the hyperbolic metric.
We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for the case of domains in the $n$-dimensional Euclidean space,…
Three-dimensional field theories with N=3 and N=4 supersymmetries are considered in the framework of the harmonic-superspace approach. Analytic superspaces of these supersymmetries are similar; however, the geometry of gauge theories with…