Search results for "Metric geometry"
showing 10 items of 222 documents
A Newman property for BLD-mappings
2019
We define a Newman property for BLD-mappings and prove that for a BLD-mapping between generalized manifolds equipped with complete path-metrics, this property is equivalent to the branch set being porous when the codomain is LLC. peerReviewed
ISOMETRY GROUPS OF WEIGHTED SPACES OF HOLOMORPHIC FUNCTIONS: TRANSITIVITY AND UNIQUENESS
2009
We survey some recent results on the isometries of weighted spaces of holomorphic functions defined on an open subset of ℂn. We will see that these isometries are determined by a subgroup of the automorphisms on a distinguished subset of the domain. We will look for weights with 'large' groups of isometries and observe that in certain circumstances the group of isometries determines the weight.
Local dimensions of measures on infinitely generated self-affine sets
2014
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.
Mappings of finite distortion and asymmetry of domains
2013
We establish an anisotropic Bonnesen inequality for images of balls under homeomorphisms with exponentially integrable distortion. Mathematics Subject Classification (2000): 30C65, 46E35.
Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples
2007
In the last few years, many works have appeared containing examples and general results on harmonicity and minimality of vector fields in different geometrical situations. This survey will be devoted to describe many of the known examples, as well as the general results from where they are obtained.
Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution
2015
We construct the time-optimal synthesis for 3 problems that are linear in the control and with polytopic constraints in the controls. Namely, the Brockett integrator, the Grushin plane, and the Martinet distribution. The main purpose is to illustrate the steps in solving an optimal control problem and in particular the use of second order conditions. The Grushin and the Martinet case are particularly important: the first is the prototype of a rank-varying distribution, the second of a non-equiregular structure.
Combinatorial proofs of two theorems of Lutz and Stull
2021
Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…
The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints
2019
Discrete Mathematics & Theoretical Computer Science ; vol. 22 no. 1 ; Automata, Logic and Semantics ; 1365-8050
The General Routing Problem polyhedron: Facets from the RPP and GTSP polyhedra
1998
[EN] In this paper we study the polyhedron associated with the General Routing Problem (GRP). This problem, first introduced by Orloff in 1974, is a generalization of both the Rural Postman Problem (RPP) and the Graphical Traveling Salesman Problem (GTSP) and, thus, is NP -hard. We describe a formulation of the problem such that from every non-trivial facet-inducing inequality for the RPP and GTSP polyhedra, we obtain facet-inducing inequalities for the GRP polyhedron, We describe a new family of facet-inducing inequalities for the GRP, the honeycomb constraints, which seem to be very useful for solving GRP and RPP instances. Finally, new classes of facets obtained by composition of facet-i…
Optimization Under Fuzzy Max-t-Norm Relation Constraints
2019
Fuzzy relation equations and inequalities play an important role in many tools of fuzzy modelling and have been extensively studied. In many practical applications they are used as constraints in optimization. Algorithms for specific objective functions have been proposed by many authors. In this paper we introduce a method to convert a system of fuzzy relation constraints with max-t-norm composition to a linear constraint system by adding integer variables. A numerical example is provided to illustrate the proposed method.