When the boundary of the curve complex is connected any quasi-isometry is bounded distance from a simplicial automorphism. As a consequence, when the boundary is connected the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.

We study the geometry of horospheres in Teichmüller space Riemann surfaces genus g with n punctures, where 3g-3+n≥2. show that every C 1 -diffeomorphism to itself preserves is an element extended mapping class group. Using relation between and metric balls, we obtain a new proof Royden’s Theorem isometry group

This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on Lebesgue space $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ $n\geq 1$. We obtain certain equivalent conditions commutativity essential these operators. In last section, we deal with spectrum a operator $L^2(\mathbb{T}^n)$ investigate such an to be isometry, hyponormal or nor...

In this note we revisit the emergent conformal symmetry in near-ring region of warped spacetime. particular, propose a novel construction $sl(2,R)_{\text{QNM}}$ symmetry. We show that each eikonal QNM family falls into one highest-weight representation algebra, and can be related to isometry group $sl(2,R)_{\text{ISO}}$ simple way. Furthermore find coherent state space identified with phase pho...

In this paper , the completion of t^ω-approach spaces, isometric in space and equivalent sequences are defined. Every normed can be embedded Banach is proved, χ ̃ an isometry ψ from onto subspace F which dense introduced, as well as, shown uniquely up to isometry. addition, what mentioned above, some essential definitions, examples, important theorems included illustrate our work.

In this paper, it is proved that every s-sparse vector x ∈ R can be exactly recovered from the measurement vector z = Ax ∈ R via some `-minimization with 0 < q ≤ 1, as soon as each s-sparse vector x ∈ R is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the `-minimization can be so chosen to be about 0.6796× (1− δ2s(A)), where δ2s(A) is the restricted isome...

We define the intersection complex for universal cover of a compact weakly special square and show that it is quasi-isometry invariant. By using this invariant, we study quasi-isometric classification 2-dimensional right-angled Artin groups planar graph 2-braid groups. Our results two well-known cases groups: (1) those whose defining graphs are trees (2) outer automorphism finite. Finally, ther...

A Banach space $X$ has the $Mazur$-$Ulam$ $property$ if any isometry from unit sphere of onto other $Y$ extends to a linear spaces $X,Y$. is called $smooth$ ball unique supporting functional at each point sphere. We prove that non-smooth 2-dimensional Mazur-Ulam property.

A continuous linear Hilbert space operator S is said to be a 2-isometry if the and its adjoint S∗ satisfy relation S∗2S2−2S∗S+I=0. We study operators having liftings or dilations 2-isometries. The of an which admits such restriction backward shift on vector-valued analytic functions. These results are applied concave similar contractions. Two types 2-isometries, as well extensions induced by th...

Let 1 and 2 be strongly pseudoconvex domains in Cn and f : 1 → 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C1 map to
̄1. We then prove that f |∂ 1 : ∂ 1 → ∂ 2 is a CR or anti-CR diffeomorphism. It follows that 1 and 2 must be biholomorphic or anti-biholomorphic. Mathematics Subject Classification (2000): 32F45 (primary); 32Q45 (secondary).