Related papers: Quasiconformal maps, analytic capacity, and non li…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

Let $M=S^{2n+1}/ \Gamma$, $\Gamma$ is a finite group which acts freely and isometrically on the $(2n+1)$-sphere and therefore $M$ is diffeomorphic to a compact space form. In this paper, we first investigate Katok's famous example about…

Using the analytic assembly map that appears in the Baum-Connes conjecture in noncommutative geometry, we generalise the $\Spin^c$-version of the Guillemin-Sternberg conjecture that `quantisation commutes with reduction' to (discrete series…

For a finite set of balls of radius $r$, the $k$-fold cover is the space covered by at least $k$ balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the $k$-fold filtration of the…

Let $(X, d)$ be a compact metric space, and let $Q \subset X$ be countable. Given functions $R: Q \to \mathbb{R}^+$ and $\phi: \mathbb{R}^+ \to \mathbb{R}^+$, we consider the set $E(Q, R, \phi)$ of points $x \in X$ that ``hit'' the…

We study the period map from infinitesimal deformations of a scheme $X$ over a perfect field $k$ to those of the associated $k$-linear $\infty$-category $\mathrm{QC}(X)$. For quasicompact, smooth, and separated $X$, we identify the…

We construct an example of a purely unrectifiable measure $\mu$ in $\mathbb{R}^d$ for which the singular integrals associated to the kernels $\displaystyle{K(x)=\frac{P_{2k+1}(x)}{|x|^{2k+d}}}$, with $k\geq 1$ and $P_{2k+1}$ a homogeneous…

The concept of hyperelastic deformations of bi-conformal energy is developed as an extension of quasiconformality. These are homeomorphisms $h:X \to Y$ between domains $ X, Y \subset \mathbb R^n$ of the Sobolev class $W^{1,n}_{loc} (X, Y)$…

We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, then all continuous real-valued functions on C(K) may be…

Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A…

Suppose that $f$ is a $K$-quasiconformal ($(K,K')$-quasiconformal resp.) self-mapping of the unit disk $\mathbb{D}$, which satisfies the following: $(1)$ the inhomogeneous polyharmonic equation $\Delta^{n}f=\Delta(\Delta^{n-1}…

To any compact $K\subset\hat{\mathbb{C}}$ we associate a map $\lambda_K: \hat{\mathbb{C}}\rightarrow\mathbb{N}\cup\{\infty\}$ -- the lambda function of $K$ -- such that a planar continuum $K$ is locally connected if and only if…

The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic…

The Bekenstein bound takes the holographic principle into the realm of flat space, promising new insights on the relation of non-gravitational physics to quantum gravity. This makes it important to obtain a precise formulation of the bound.…

We introduce the notion of translational Riemannian manifolds and define a Gauss map for orientable immersed hypersurfaces lying in these ambients, an associated translational curvature and prove a Gauss-Bonnet theorem. We also use this…

We study a Floer-theoretic approach to harmonic maps from the two-torus into non-flat K\"ahler manifolds. Building on the complex-regularized polysymplectic (CRPS) formalism of [BF24], which provides a Hamiltonian description of harmonic…

Let $ T:[0,1]\to[0,1] $ be an expanding Markov map with a finite partition. Let $ \mu_\phi $ be the invariant Gibbs measure associated with a H\"older continuous potential $ \phi $. In this paper, we investigate the size of the uniform…

The isoperimetric inequality for a smooth compact Riemannian manifold $A$ provides a positive ${\bf c}(A)$, so that for any $k+1$ dimensional integral current $S_0$ in $A$ there exists an integral current $ S$ in $A$ with $\partial…

We extend a well-known theorem by Jones and Makarov [JM] on the singularity of boundary distortion of planar conformal mappings. We use a different technique to recover the previous result and, moreover, generalize the result for…

The Katz-Sarnak Density Conjecture states that the behavior of zeros of a family of $L$-functions near the central point (as the conductors tend to zero) agrees with the behavior of eigenvalues near 1 of a classical compact group (as the…