Related papers: On McMullen's algorithm for the Hausdorff dimensio…
We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific…
We consider (bounded) Besicovitch sets in the Heisenberg group and prove that $L^p$ estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.
In this paper we prove some lower bounds on the Hausdorff dimension of sets of Furstenberg type. Moreover, we extend these results to sets of generalized Furstenberg type, associated to doubling dimension functions. With some additional…
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of…
Recently, Kronqvist et al.~\cite{KronqvistLundellWesterlund2016} rediscovered the supporting hyperplane algorithm of Veinott~\cite{Veinott1967} and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs.…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational…
We prove a sharp upper bound on the Hausdorff dimension of weighted singular vectors in $\mathbb{R}^m$ using dynamics on homogeneous spaces, specifically the method of integral inequalities. Together with the lower bound proved recently by…
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using…
Suppose G is a hyperbolic group whose boundary has topological dimension k. If the boundary is quasisymmetrically homeomorphic to an Ahlfors k-regular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice…
We study the compactness in $L^{1}_{loc}$ of the semigroup mapping $(S_t)_{t > 0}$ defining entropy weak solutions of general hyperbolic systems of conservation laws in one space dimension. We establish a lower estimate for the Kolmogorov…
For Cantor circle Julia sets of hyperbolic rational maps, we prove that they are quasisymmetrically equivalent to standard Cantor circles (i.e., connected components are round circles). This gives a quasisymmetric uniformization of all…
We associate convex bodies to a wide class of graded G-algebras where G is a connected reductive group. These convex bodies give information about the Hilbert function as well as multiplicities of irreducible representations appearing in…
We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We…
Central to the theory of special cube complexes is Haglund and Wise's construction of the canonical completion and retraction, which enables one to build finite covers of special cube complexes in a highly controlled manner. In this paper…
We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof…
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover we show the…
Consider all the level sets of a real function. We can group these level sets according to their Hausdorff dimensions. We show that the Hausdorff dimension of the collection of all level sets of a given Hausdorff dimension can be…
An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…