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PLANE WITH $A_{\infty}$ -WEIGHTED METRIC NOT BILIPSCHITZ EMBEDDABLE TO ${\bb R}^n$

2002; Wiley; Volume: 34; Issue: 06 Linguagem: Inglês

10.1112/s0024609302001200

1469-2120

Tomi Laakso,

Geometric Analysis and Curvature Flows

Bulletin of the London Mathematical SocietyVolume 34, Issue 6 p. 667-676 Notes and papers Plane with A∞-Weighted Metric not Bilipschitz Embeddable to Rn Tomi J. Laakso, Tomi J. Laakso Department of Mathematics, P.O. Box 4 (Yliopistonk. 5), FIN-00014, University of Helsinki, Finland [email protected]Search for more papers by this author Tomi J. Laakso, Tomi J. Laakso Department of Mathematics, P.O. Box 4 (Yliopistonk. 5), FIN-00014, University of Helsinki, Finland [email protected]Search for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024609302001200Citations: 46AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A planar set G ⊂ R2 is constructed that is bilipschitz equivalent to (G,dz), where (G, d) is not bilipschitz embeddable to any uniformly convex Banach space. Here, Z ∈ (0, 1) and dz denotes the zth power of the metric d. This proves the existence of a strong A∞ weight in R2, 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 R2. 2000 Mathematics Subject Classification 54E40 (primary); 30C62, 30C65, 28A80 (secondary). Citing Literature Volume34, Issue6November 2002Pages 667-676 RelatedInformation