The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, w...

Let V be an n-dimensional vector space over a finite field Fq. We consider on V the π-metric dπ recently introduced by K. Feng, L. Xu and F. J. Hickernell. In this paper we give a complete description of the group of symmetries of the metric space (V, dπ).

It is shown that —over Bishop's constructive mathematics— the indecomposability of R is equivalent to the statement that all functions from a complete metric space into a metric space are sequentially nondiscontinuous. Furthermore we prove that the indecomposability of R \ {0} is equivalent to the negation of the disjunctive version of Markov's Principle. These results contribute to the program...

The paper generalises Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. Additionally, in the rational case, the resulting distance is filtering invariant and can be computed efficiently.

Using the concept of D-metric we prove some common fixed point theorems for generalized contractive mappings on a complete D-metric space. Our results extend, improve, and unify results of Fisher and´Ciri´c.

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

One of the main purpose of this paper is to compare those well-known canonical and complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new metrics, the Ricci metric and the perturbed Ricci metric. We will prove that these metrics are equivalent to those classical complete metrics. For this purpose we study in detail the asymptotic behaviors and th...

It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete R-tree; (ii) M is hyperconvex and has unique metric segments.

The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,+∞)ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provid...