Live briefing
Everything about Busemann function
In geometric topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds. 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". Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Busemann functionA 5-minute orientation
- Skim a recent paper: Busemann functions and uniformization of Gromov hyperbolic spacesInfluential work since 2022
- Read the landmark paper: Non-expanding maps and Busemann functionsCited 47 times
- Go sideways: CAT(k) spaceA closely related topic
- Go sideways: Hyperbolic metric spaceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- Definition and elementary properties
- Example: Poincaré disk
- Busemann functions on a Hadamard space
- Bordification of a Hadamard space
- Busemann functions on a Hadamard manifold
- Compactification of a proper Hadamard space
- Quasigeodesics in the Poincaré disk, CAT(-1) and hyperbolic spaces
- Efremovich–Tikhomirova theorem
- Busemann functions and visual metrics for CAT(-1) spaces
- Applications in percolation theory
🏆 Landmark papers (most cited)
Non-expanding maps and Busemann functions
Regularity of Lorentzian Busemann Functions
Busemann Functions in a Harmonic Manifold
Extremal convex sets for Sylvester–Busemann type functionals
Busemann functions and total curvature
A Functional Busemann Intersection Inequality
Busemann Functions for the N-Body Problem
Some Results about the Level Sets of Lorentzian Busemann Function and Bartnik’s Conjecture
🆕 Influential since 2022
Busemann functions and uniformization of Gromov hyperbolic spaces
Sylvester–Busemann Type Functionals with Respect to Orlicz Centroid Bodies
The Busemann-Petty problem on entropy of log-concave functions
Fenchel Conjugate via Busemann Function on Hadamard Manifolds
Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials
📚 Books worth reading
Open Library didn't respond; try again in a moment.
🔗 Related topics
- CAT(k) space In mathematics, a 𝐂𝐀𝐓(k) space, where k is a real number, is a specific type of metric space. Intuitively, triangles in a CAT(k) space (with k<0) are…
- Hyperbolic metric space In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number…
- Period mapping In mathematics, in the field of algebraic geometry, the period mapping relates families of Kähler manifolds to families of Hodge structures. Let f : X…
- Glossary of Riemannian and metric geometry This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following…
- Continuous function In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies…
- Ergodic flow In mathematics, ergodic flows occur in geometry, through the geodesic and horocycle flows of closed hyperbolic surfaces. Both of these examples have been…
- Directional derivative In multivariable calculus, the directional derivative measures the instantaneous rate at which a function changes along a specified vector through a given…
- Intrinsic metric In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other…