Introduction. The primary aim of this report is to present a broad outline for a coherent geometric theory of certain aspects of nonlinear functional analysis. Its setting requires the calculus in topological vector spaces, differential geometry of infinite dimensional manifolds, and the algebraic and differential topology of function spaces. For the most part the developments are of quite rece...

With the rise in prominence of high dimensional data, multivariate measures of center have become very important. In this paper we focus on one multivariate measure of center the geometric median, which is defined as the minimizer of the sum of distances to the data points. We study the quantitative robustness of the geometric median. Showing that for a non-degenerate distribution of N points, ...

Quasiconformalmappings are generalizations of conformalmappings. They can be considered not only on Riemann surfaces, but also on Riemannian manifolds in all dimensions, andevenon arbitrarymetric spaces. Quasiconformal mappings occur naturally in various mathematicalandoftenaprioriunrelatedcontexts. The importance of quasiconformal mappings in complex analysis was realized by Ahlfors and Teichm...

In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment for plausibilities and commonalities, we exploit it to understand the simplicial form of both plaus...

This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, “p-typical” Witt vectors of p-adic schemes of finite type are already reasonably well understood. The main point here is to generalize this theory in two ways. We allow not just p-typical Witt vectors but those taken with respect to any set of primes in any ring of integers in any global field, fo...

In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment for plausibilities and commonalities, we exploit it to understand the simplicial form of both plaus...

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For symmetric spaces of higher rank, which contain isometrically embedded Euclidean...

In this paper we study biholomorphic maps between Teichmüller spaces and the induced linear isometries between the corresponding tangent spaces. The first main result in this paper is the following classification theorem. If M and N are two Riemann surfaces that are not of exceptional type, and if there exists a biholomorphic map between the corresponding Teichmüller spaces Teich(M) and Teich(N...

We study the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza–Klein type) spaces. The problem of definition of spinors on generalized Finsler spaces is solved in the framework of the geometry of Clifford ...

We show that the centraliser of the space of n-fold symmetric injective tensors, n ≥ 2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spac...