Related papers: Strengthened Grunsky and Milin inequalities
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties of holomorphic motions over almost…
Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.
This article is the introductory part of authors PhD thesis. The article presents a new coordinate invariant definition of quasiregular and quasiconformal mappings on Riemannian manifolds that generalizes the definition of quasiregular…
The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its Klain function is characterized. Among several applications, it is shown that…
We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii…
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain a simple characterization that involves Lipschitz functions…
We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that…
A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.
We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are…
Quasiregular mappings $f:\Omega\subset\R^{n}\to \R^{n}$ are a natural generalization of analytic functions from complex analysis and provide a theory which is rich with new phenomena. In this paper we extend a well-known result of A.~Chang…
We present a new and simple proof of Teichm\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular…
The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations…
The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly…
We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of…
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…
In this paper, we study inequalities involving polynomials and quasimodular forms. More precisely, we focus on the monotonicity of the functions of the form $t \mapsto t^m F(it)$ where $F$ is a quasimodular form and $m > 0$. As an…
In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm…
We present a geometric approach to a well-known sharp inequality, due to Cowen and Pommerenke, about angular derivatives of general univalent self-maps of the unit disk.