We establish a structure theorem for minimizing sequences the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under sole (necessary) assumption that measure of unit balls is uniformly bounded away from zero, we prove limit such sequence identified by finite collection regions possibly contained in pointed Gromov--Hausdorff limits ambient space $X$ ...

The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.

There are various notions of “boundaries at infinity” of metric spaces in the literature. Perhaps the best known is the ideal boundary ∂IX defined using geodesic rays, and particularly studied for the classes of CAT(0) and proper geodesic Gromov hyperbolic spaces. Closely related to this is the concept of a Gromov boundary ∂GX defined using Gromov sequences (or “sequences converging to infinity...

The crepant resolution conjecture states that the Gromov–Witten invariants of an orbifold X should be determined in a precise way by the Gromov–Witten invariants of a crepant resolution of its coarse moduli space. We compute the Gromov–Witten invariants of the stack symmetric square of P 2 and compare them with the Gromov– Witten invariants of its crepant resolution, Hilb 2 P 2 (which were comp...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

We build the network of the top 190 Italian quoted companies during the two financial crises of 2008-2009 (US credit crisis) and 2010-2011 (European sovereign debt crisis) and compare its structure to the pre-crises years, using both minimum spanning trees and the full network with thresholds. We also analyze the centrality and compactness of industry sectors. We find a general contraction of t...

In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics betw...

Given a manifold M and a proper sub-bundle ∆ ⊂ TM , we study homotopy properties of the horizontal base-point free loop space Λ, i.e. the space of absolutely continuous maps γ : S → M whose velocities are constrained to ∆ (for example: legendrian knots in a contact manifold). A key technical ingredient for our study is the proof that the base-point map F : Λ → M (the map associating to every lo...

The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology class models growing random graphs that generalises Remy's algorithm binary trees. We describe the obtained limits using some iterative gluing construction famous line-breaking Aldous' Brownian tree. In order do that, we framework which metric space constructed by smaller s...