WebEnter the email address you signed up with and we'll email you a reset link. In geometric topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds (simply connected complete Riemannian manifolds of nonpositive curvature). They are named after Herbert Busemann, who … See more In a Hadamard space, where any two points are joined by a unique geodesic segment, the function $${\displaystyle F=F_{t}}$$ is convex, i.e. convex on geodesic segments $${\displaystyle [x,y]}$$. … See more Suppose that x, y are points in a Hadamard manifold and let γ(s) be the geodesic through x with γ(0) = y. This geodesic cuts the boundary of the closed ball B(y,r) at the two points γ(±r). Thus if d(x,y) > r, there are points u, v with d(y,u) = d(y,v) = r such … See more Morse–Mostow lemma In the case of spaces of negative curvature, such as the Poincaré disk, CAT(-1) and hyperbolic spaces, there is a metric structure on their Gromov boundary. This structure is preserved by the group of quasi … See more In the previous section it was shown that if X is a Hadamard space and x0 is a fixed point in X then the union of the space of Busemann functions vanishing at x0 and the space of functions hy(x) = d(x,y) − d(x0,y) is closed under taking uniform limits on bounded … See more Eberlein & O'Neill (1973) defined a compactification of a Hadamard manifold X which uses Busemann functions. Their construction, which can be extended more generally to proper (i.e. locally compact) Hadamard spaces, gives an explicit geometric … See more Before discussing CAT(-1) spaces, this section will describe the Efremovich–Tikhomirova theorem for the unit disk D with the Poincaré metric. It asserts that quasi … See more Busemann functions can be used to determine special visual metrics on the class of CAT(-1) spaces. These are complete geodesic metric spaces in which the distances between points on the boundary of a geodesic triangle are less than or equal to the … See more

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WebBusemann points. The horofunction boundary is a natural way to embed a, possibly non-proper,metricspaceintoacompacttopologicalspace.Ingeneralthehorofunctionboundaryis … WebBusemann [8], Guggenheimer [13, 12] and Petty [23]. They were used to study concepts of curvatures (and curve theory, in general), and they also appeared when studying … slow cooker sweet potato curry

[math/0309291] Busemann Points of Infinite Graphs - arXiv

Web192 C. Walsh Proposition 2.1. Let 1 and 2 be two geodesics in a finitely-generated group. The following are equivalent: (i) 1 and 2 converge to the same Busemann point; (ii) for … Webin the sense of Busemann, and it was proved by Masur and Wolf [16] that the Teichmu¨ller metric is not Gromov hyperbolic. For more progress in the ... Teichmu¨ller geodesic rays from a fixed base-point. Extending the home-omorphism to the closed ball defines a compactificaiton of T(S), which is WebAdolf Busemann (20 April 1901 – 3 November 1986) was a German aerospace engineer and influential Nazi-era pioneer in aerodynamics, specialising in supersonic airflows. He introduced the concept of swept … soft tissue massage near me