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Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm…
We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously…
In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
We construct a family of purely PI unrectifiable Lipschitz differentiability spaces and investigate the possible of Banach spaces targets for which Lipschitz differentiability holds. We provide a general investigation into the geometry of…
A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…
In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--R\"{o}hrle, the usual notion of $G$-complete reducibility can be…
Finite difference schemes in the spatial variable for degenerate stochastic parabolic PDEs are investigated. Sharp results on the rate of $L_p$ and almost sure convergence of the finite difference approximations are presented and results on…
We show that rough isometries between metric spaces X, Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough…
We construct a (Lipschitz) differentiability space which has at generic points a disconnected tangent and thus does not contain positive measure subsets isometric to positive measure subsets of spaces admitting a Poincar\'e inequality. We…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone…
The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the…
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally…
In this note we study the differentiability with respect to the time-parameter of semigroups consisting of Lipschitzian or smooth self-mappings of a domain in a Banach space.
The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…
In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense…
Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective,…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…