About: Busemann function

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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 introduced them; he gave an extensive treatment of the topic in his 1955 book "The geometry of geodesics".

Attributes	Values
rdfs:label	Busemann function (en) Busemann-Funktion (de) Функция Буземана (ru)
rdfs:comment	In der Riemannschen Geometrie, einem Teilgebiet der Mathematik, ist die Busemann-Funktion eine Funktion, die den "Abstand zu unendlich fernen Punkten" misst. Sie ist nach Herbert Busemann benannt. (de) 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 introduced them; he gave an extensive treatment of the topic in his 1955 book "The geometry of geodesics". (en) Функция Буземана — определённый тип функций на метрическом пространстве. Грубо говоря, функцию Буземана можно рассматривать как «расстояние до бесконечно удалённой точки». (ru)
dcterms:subject	Geometry
Wikipage page ID	2850640 (xsd:integer)
Wikipage revision ID	1115502564 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartan-Hadamard theorem Quasiconformal mapping Mostow rigidity theorem Anharmonic group Hyperbolic metric space Douady–Earle extension Geometric topology Equicontinuous George Mostow Möbius transformation Connected space Cross-ratio Lipschitz function Comparison triangle Yurii Reshetnyak Journal d'Analyse Mathématique Symmetric space Geometry Hadamard manifold Hadamard space Hausdorff distance Gradient vector field American Mathematical Society Dini's theorem Gradient flow Probability theory Quasisymmetric map Ray (geometry) Riemannian manifold Harvard University Hilbert space Arzelà–Ascoli theorem Birkhäuser Herbert Busemann Marston Morse Hölder continuous Incircle Metric space Orthogonal projection European Mathematical Society Poisson kernel First passage percolation Poincare disk model Proper metric space Simply connected North-Holland Publishing Company Cross ratio Quasigeodesic Mutatis mutandi Teichmüller theory
Link from a Wikipage to an external page	http://www.mathnet.ru/php/getFT.phtml%3Fjrnid=im&paperid=3046&what=fullt&option_lang=eng%7Clanguage=ru https://web.archive.org/web/20060708074249/http:/www.math.harvard.edu/~lurie/papers/hadamard.pdf https://www.ams.org/journals/tran/1924-026-01/S0002-9947-1924-1501263-9/S0002-9947-1924-1501263-9.pdf%7Cdoi=10.1090/s0002-9947-1924-1501263-9%7Cdoi-access=free https://www.ams.org/journals/tran/1957-084-01/S0002-9947-1957-0083024-5/S0002-9947-1957-0083024-5.pdf%7Cdoi=10.1090/s0002-9947-1957-0083024-5%7Cdoi-access=free http://www.math.harvard.edu/~lurie/papers/hadamard.pdf http://msp.org/pjm/2012/259-1/pjm-v259-n1-p03-s.pdf%7Cdoi=10.2140/pjm.2012.259.55%7Carxiv=1010.6028%7Cs2cid=
sameAs	Busemann function Busemann function Busemann function Busemann function Busemann function
dbp:wikiPageUsesTemplate	dbt:! dbt:Citation dbt:Cite_book dbt:Harvtxt dbt:Math dbt:More_citations dbt:Multiple_issues dbt:Overline dbt:Pi dbt:Radic dbt:Reflist dbt:See dbt:Technical dbt:Format_footnotes dbt:Norm dbt:Mset dbt:SpringerEOM
first	T. (en)
id	Busemann_function&oldid=13719 (en)
last	Shioya (en)
title	Busemann function (en)
has abstract	In der Riemannschen Geometrie, einem Teilgebiet der Mathematik, ist die Busemann-Funktion eine Funktion, die den "Abstand zu unendlich fernen Punkten" misst. Sie ist nach Herbert Busemann benannt. (de) 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 introduced them; he gave an extensive treatment of the topic in his 1955 book "The geometry of geodesics". (en) Функция Буземана — определённый тип функций на метрическом пространстве. Грубо говоря, функцию Буземана можно рассматривать как «расстояние до бесконечно удалённой точки». (ru)
prov:wasDerivedFrom	wikipedia-en:Busemann_function?oldid=1115502564&ns=0
page length (characters) of wiki page	91407 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Busemann_function
is Link from a Wikipage to another Wikipage of	Morse–Mostow lemma Hyperbolic metric space Morse-Mostow lemma

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