An explicit solution of the Lipschitz extension problem

Proceedings of the American Mathematical Society

Volumn 136, Issue 12, 2008, Pages 4329-4338

  Oberman, Adam M ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Absolute minimizers; Infinity Laplacian; Lipschitz extension

Indexed keywords

EID: 77950615708     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-08-09457-4     Document Type: Article

References (15)

1. [ACJ04] Gunnar Aronsson, Michael G. Crandall, and Petri Juutinen. A tour of the theory of absolutely minimizing functions. Bull. Amer. Math. Soc. (N.S.), 41(4):439-505 (electronic), 2004. MR2083637 (2005k:35159)
2. [Aro67] Gunnar Aronsson. Extension of functions satisfying Lipschitz conditions. Ark. Mat., 6:551-561, 1967. MR0217665 (36:754)
3. [Ber03] Dimitri P. Bertsekas. Convex analysis and optimization. Athena Scientific, Belmont, MA, 2003. With Angelia Nedić and Asuman E. Ozdaglar. MR2184037 (2006j:90001)
4. [CMS98] Vicent Caselles, Jean-Michel Morel, and Catalina Sbert. An axiomatic approach to image interpolation. IEEE Trans. Image Process., 7(3):376-386, 1998. MR1669524 (2000d:94001)
5. [Juu02] Petri Juutinen. Absolutely minimizing Lipschitz extensions on a metric space. Ann. Acad. Sci. Fenn. Math., 27(1):57-67, 2002. MR1884349 (2002m:54020)
6. [Kir34] M. D. Kirszbraun. Uber die zusammenziehenden und Lipschitzchen Transformationen. Fund. Math., 22:77-108, 1934.
7. [LG04] E. Le Gruyer. On absolutely minimizing Lipschitz extensions. http://arxiv.org/abs/math/0403158v1, 2004.
8. [LGA96] E. Le Gruyer and J. C. Archer. Stability and convergence of extension schemes to continuous functions in general metric spaces. SIAM J. Math. Anal., 27(1):274-285, 1996. MR1373157 (96k:41002)
9. [LGA98] E. Le Gruyer and J. C. Archer. Harmonious extensions. SIAM J. Math. Anal., 29(1):279-292 (electronic), 1998. MR1617186 (99d:54008)
10. [LN05] James R. Lee and Assaf Naor. Extending Lipschitz functions via random metric partitions. Invent. Math., 160(1):59-95, 2005. MR2129708 (2006c:54013)
11. [LS97] U. Lang and V. Schroeder. Kirszbraun's theorem and metric spaces of bounded curvature. Geom. Funct. Anal., 7(3):535-560, 1997. MR1466337 (98d:53062)
12. [McS34] Edward James McShane. Extension of range of functions. Bull. Amer. Math. Soc., 40:837-842, 1934. MR1562984
13. [MN06] Manor Mendel and Assaf Naor. Some applications of Ball's extension theorem. Proc. Amer. Math. Soc., 134(9):2577-2584 (electronic), 2006. MR2213735 (2007a:46014)
14. [MST06] Facundo Memoli, Guillermo Sapiro, and Paul Thompson. Brain and surface warping via minimizing Lipschitz extensions. IMA Preprint Series 2092, January 2006.
15. [Obe05] Adam M. Oberman. A convergent difference scheme for the infinity Laplacian: Construction of absolutely minimizing Lipschitz extensions. Math. Comp., 74(251):1217-1230 (electronic), 2005. MR2137000 (2006h:65165)