Premium
Plane with A ∞ ‐Weighted Metric not Bilipschitz Embeddable to R n
Author(s) -
Laakso Tomi J.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001200
Subject(s) - mathematics , regular polygon , jacobian matrix and determinant , banach space , compact space , plane (geometry) , pure mathematics , metric (unit) , mathematical analysis , planar , metric space , combinatorics , geometry , operations management , computer graphics (images) , computer science , economics
A planar set G ⊂ R 2 is constructed that is bilipschitz equivalent to ( G , d z ), where ( G, d ) is not bilipschitz embeddable to any uniformly convex Banach space. Here, Z ∈ (0, 1) and d z denotes the z th power of the metric d . This proves the existence of a strong A ∞ weight in R 2 , such that the corresponding deformed geometry admits no bilipschitz mappings to any uniformly convex Banach space. Such a weight cannot be comparable to the Jacobian of a quasiconformal self‐mapping of R 2 . 2000 Mathematics Subject Classification 54E40 (primary); 30C62, 30C65, 28A80 (secondary).
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom