Related papers: The open mapping theorem for regular quaternionic …
Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field…
We employ tools from complex analysis to construct the $*$-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the $*$-exponential; we…
Given a function $f: (a,b) \rightarrow \mathbb{R},$ L\"owner's theorem states $f$ is monotone when extended to self-adjoint matrices via the functional calculus, if and only if $f$ extends to a self-map of the complex upper half plane. In…
We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental…
The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of…
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
We introduce a notion of locally approximable continuous CR functions on locally closed subsets of reduced complex spaces, generalizing both holomorphic functions and CR functions on CR submanifolds. Under additional assumptions of…
Douglas and Rudin proved that any unimodular function on the unit circle $\T$ can be uniformly approximated by quotients of inner functions. We extend this result to the operator-valued unimodular functions defined on the boundary of the…
After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as…
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important…
This short note first develops a general formalism for globally removing a factor from an obstruction theory. This formalism is then applied to give a construction of a reduced obstruction theory on the moduli of maps from a curve to a…
In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…
We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for \Gamma_0(2). Numerical evidence indicates that a sharper bound holds for the…
The property of a normal functor to be open-multicommutative proposed by Kozhan and Zarichnyi (2004) is investigated. A number of normal functors related to the functor of probability measures and equipped with convex structure are…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
The paper extends the well-known Lyusternik-Graves theorem for set-valued mappings to the Holder framework, offers an affirmative answer to an open problem proposed by Dontchev and improves recent results of He and Ng. Primal and dual…