BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces (2015)
- Volume: 3, Issue: 1, page 231-243, electronic only
- ISSN: 2299-3274
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top- [1] E. Breuillard. Geometry of locally compact groups of polynomial growth and shape of large balls, 2007. arXiv:0704.0095. Zbl1310.22005
- [2] M. Christ. A T(b) theorem with remarks on analytic capacity and the Cauchy integral. Colloq.Math., 60/61(2):601–628, 1990. Zbl0758.42009
- [3] G. David. Morceaux de graphes Lipschitziens et intégrales singulières sur un surface. Rev. Mat. Iberoam., 4(1):73–114, 1988. [Crossref] Zbl0696.42011
- [4] G. David. Wavelets and singular integrals on curves and surfaces, volume 1465 of Lecture Notes in Mathematics. Springer- Verlag, 1991.
- [5] G. David and S. Semmes. Quantitative rectifiability and Lipschitz mappings. Trans. Amer. Math. Soc., 337(2):855–889, 1993. Zbl0792.49029
- [6] G.C. David. Bi-Lipschitz pieces between manifolds. Rev. Mat. Iberoam. To appear. Zbl1342.28007
- [7] Y. Guivarc’h. Croissance polynômiale et périodes des fonctions harmoniques. Bull. Sc. Math. France, 101:353–379, 1973. Zbl0294.43003
- [8] J. Heinonen and S. Semmes. Thirty-three yes or no questions about mappings, measures, and metrics. Conform. Geom. Dyn., 1:1–12, 1997. [Crossref] Zbl0885.00006
- [9] P. Jones. Lipschitz and bi-Lipschitz functions. Rev. Mat. Iberoam., 4(1):115–121, 1988. [Crossref] Zbl0782.26007
- [10] E. Le Donne. A metric characterization of Carnot groups. Proc. Amer. Math. Soc., 132:845–849, 2015. Zbl1307.53027
- [11] E. Le Donne, S. Li, and T. Rajala. Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces, 2015. Preprint.
- [12] S. Li. Coarse differentiation and quantitative nonembeddability for Carnot groups. J. Funct. Anal., 266:4616–4704, 2014. [WoS] Zbl1311.46021
- [13] V. Magnani. Differentiability and area formula on stratified Lie groups. Houston J. Math., 27(2):297–323, 2001. Zbl0983.22009
- [14] W. Meyerson. Lipschitz and bilipschitz maps on Carnot groups. Pac. J. Math, 263(1):143–170, 2013. [WoS] Zbl1295.43009
- [15] R. Montgomery. A tour of sub-Riemannian geometries, their geodesics and applications, volume 91 of Mathematical Surveys and Monographs. American Mathematical Society, 2002.
- [16] P. Pansu. Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann.Math. (2), 129(1):1– 60, 1989. Zbl0678.53042
- [17] R. Schul. Ahlfors-regular curves in metric spaces. Ann. Acad. Sci. Fenn. Math., 32:437–460, 2007. Zbl1122.28006
- [18] R. Schul. Bi-Lipschitz decomposition of Lipschitz functions into a metric space. Rev. Mat. Iberoam., 25(2):521–531, 2009. [Crossref] Zbl1228.28004