Busemann cocycle
WebBusemann cocycle WG ! Rdetermines a natural “logarithmic scale” on the bound-ary of the Cayley graph equal to the associated Gromov product. Its value `. 1; 2/is equal to minimum of the value of along a geodesic path connecting 1and 2in the Cayley graph of G. Using the Cayley graph of the dual groupoid G> instead, we get WebJan 1, 2000 · The paper is devoted to the study of the basic ergodic properties (ergodicity and conservativity) of the horocycle flow on surfaces of constant negative curvature with respect to the Liouville invariant measure. We give several criteria for ergodicity ...
Busemann cocycle
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WebSince Busemann functions are invariant by isometries, so are horospheres, and they pass to the quotient T1M. We introduce the notation ˘(x;y) := b V(y;˘)(x); that we will use later. This quantity is equal to the distance between the horocycles centered at ˘passing through xand y. It is called a Busemann cocycle and it depends http://homepages.math.uic.edu/~furman/preprints/hyp-erg.pdf
WebMar 4, 2024 · Our approach consists of proving a general concentration type result for cocycles satisfying a certain cohomological equation. This is line with Gordin’s method for proving the central limit theorem where the values of cocycles along random walks coming from group actions are related to martingales via a Poisson type equation. WebBusemann cocycle centered at x is defined for any two points p and q in M˜ by B x(p,q) = lim r→x dist(p,r)−dist(q,r). The horosphere centered at x and based at p is the level set {q ∈ M˜ ; B x(p,q)= 0}. LetΓbe a torsion-free discrete group of isometries of M˜ . …
WebLet be a locally convex subset of a negatively curved Riemannian manifold . We define the skinning measure on the outer unit normal bundle to in by pulling back the Patterson-Sullivan measures at infinity, and give… WebBusemann. Busemann is a German surname. Notable people with the surname include: Adolf Busemann (1901–1986), German-American aerospace engineer, inventor of …
WebAug 2, 2016 · The cocycles define stationary percolation models that can be coupled with the original one. The coupling, ergodicity, and local regularity of the limit shape give the …
WebNov 12, 2016 · The exponential of the Busemann cocycle plays the role of the Poisson kernel: we called 0-harmonic this type of functions. F-harmonic functions There are weighted versions of these equidistribution problems (see Sect. 6.3 for the details) which led to introduce the notion of F-harmonic functions. god\u0027s shoes married with childrenWebBusemann cocycle ˙: G X!R (see Sections 2.4 and 3.2), we are re-duced to prove, for every xin X, a central limit theorem (Theorem 4.7) for the random variables ˙(g n g 1;x). … book of obituaries wroe annWebApr 7, 2024 · The norm of the Busemann cocycle is asymptotically linear with respect to square root of the distance between any two vertices. Independently, Gournay and … book of oberonIn 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 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 … 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-isometries of D extend to quasi-Möbius homeomorphisms of the unit disk with the … 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 … 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 … See more Morse–Mostow lemma In the case of spaces of negative curvature, such as the Poincaré disk, CAT(-1) and … 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 … See more god\u0027s silliest goose shirtWeb(Busemann cocycle) A general version of Theorem1.1will be proved in Theorem4.1where the displacement d(z n;o) is replaced with the Busemann cocycle ˙(L n;x) of L n based at any point of xin the horofunction compacti cation of X. See also Question4.8for an ensuing problem. 2. (Translation distance) Thanks to [6, Theorem 1.3], when has bounded ... god\u0027s silence franz wrightWebTopology seminar: Marked length pattern rigidity and Busemann cocycle. Yanlong Hao. News & Events; All News; All Events; Thursday, April 6, 2024 3:00-4:00 PM 3866 East … god\u0027s signature pattern lightning treeWebThe paper is devoted to the study of the basic ergodic properties (ergodicity and conservativity) of the horocycle flow on surfaces of constant negative curvature with … book of objectives