In this article we show that any finite cover of the moduli space of closed Riemann surfaces of g genus with g > 2 does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which is equivalent to the Teichmüller metric, on any finite cover of the moduli space is ...

We introduce and study a natural notion of probabilistic 1Lipschitz maps. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic metric space G is also a probabilistic metric space. Moreover, when G is a group, then the space of all probabilistic 1-Lipschitz maps defined on G can be endowed with a monoid structure. Then, we caracterize the probabilistic invaria...

In this paper, we show that the metric space (Q,G) is a positivelycurved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of (Q, G). Then we give a decomposition of this metric space according to the signature of points in Q. Some properties of this decomposition are shown. The second part of this paper is devoted to some basi...

In this paper, we show that the metric space (Q,G) is a positivelycurved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of (Q, G). Then we give a stratification of this metric space according to the signature of points in Q. Some properties of this stratification are shown. The second part of this paper is devoted to some ba...

The notion of dislocated quasi metric space was initiated by F. M. Zeyada, G. H. Hassan and M. A. Ahmed[18] in 2006. It is a generalization due to P. Hitzler and A. K. Seda[7] in dislocated metric. Dislocated quasi metric space differs from d islocated metric space with symmetric property. After the establishment of d islocated quasi metric space, it has emerged as important area of research ac...

In the present paper, we introduces the notion of integral type contractive mapping with respect to ordered S-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered S-metric space. Moreover, we give an example to support our main result.

‎in this paper‎, ‎generalized convex contractions on orthogonal metric spaces are stablished in whath might be called their definitive versions‎. ‎also, we show that‎ there are examples which show that our main theorems are genuine generalizations of theorem 3.1 and 3.2 of cite{r}‎[ m.a. miandaragh, m. postolache, s. rezapour, ‎textit{approximate fixed points of generalizedconvex contractions},...

1 1 INTRODUCTION 2 1 Introduction Classical calculus is a basic tool in analysis. We use it so often that we forget that its construction needed considerable time and effort. Especially in the last decade, the progresses made in the field of analysis in metric spaces make us reconsider this calculus. Along this line of thought, all started with the definition of Pansu derivative [24] and its ve...

We present the ‘Basic S*’ algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, G, which is constructed as a discrete representation of an underlying configuration space (a larger “continuous” space/manifold typically of dimension greater than one), we consider the Rips complex, R(G), associated with it. Such a complex, and hence shortes...