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Book Review

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MathSciNet review: 2139304
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Luca Capogna, Carlos E. Kenig and Loredana Lanzani
Title: Harmonic measure: Geometric and analytic points of view
Additional book information: University Lecture Series, vol. 35, Amer. Math. Soc., Providence, RI, 2005, x+155 pp., ISBN 978-0-8218-3920-1, US$28.00

References [Enhancements On Off] (What's this?)

  • [AC] Alt, H. W., and Caffarelli, L., Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math., 325 (1981), 105-144. MR 618549 (83a:49011)
  • [B] Capogna, Luca; Kenig, Carlos E.; and Lanzani, Loredana, Harmonic Measure: Geometric and Analytic Points of View, University Lecture Series 35, American Mathematical Society, 2005. MR 2139304 (2006a:31002)
  • [BCGJ] Bishop, C. J.; Carleson, L.; Garnett, J.; and Jones, P. W., Harmonic measures supported on curves, Pac. J. Math., 138 (1989), 233-236. MR 996199 (90d:30069)
  • [BJ] Bishop, C. J., and Jones, P. W., Harmonic measure, $ L^2$ estimates and the Schwarzian derivative, J. Anal. Math., 62 (1994), 77-113. MR 1269200 (95f:30034)
  • [DJ] David, G., and Jerison, D. S., Lipschitz approximation to hypersurfaces, harmonic measure and singular integrals, Indiana Math. J., 39 (1990), 831-846. MR 1078740 (92b:42021)
  • [DKT] David, G.; Kenig, C. E.; and Toro, T., Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant, Comm. Pure Appl. Math., 54 (2001), no. 4, 385-449. MR 1808649 (2002g:28007)
  • [EG] Evans, L. C., and Gariepy, R., Measure theory and fine properties of functions, CRC Press, Boca Raton, FL, 1992. MR 1158660 (93f:28001)
  • [GM] Garnett, J. B., and Marshall, D. E., Harmonic measure, Cambridge U. Press, 2005. MR 2150803 (2006g:31002)
  • [J] Jerison, D., Regularity of the Poisson kernel and free boundary problems, Colloq. Math., 60-61 (1990), 547-567. MR 1096396 (92b:35177)
  • [JK] Jerison, D., and Kenig, C. E., Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. in Math., 46 (1982), 90-147. MR 676988 (84d:31005b)
  • [KT1] Kenig, C. E., and Toro, T., Harmonic measure on locally flat domains, Duke Math. J., 87 (1997), 509-551. MR 1446617 (98k:31010)
  • [KT2] Kenig, C. E., and Toro, T., Free boundary regularity for harmonic measures and Poisson kernels, Ann. of Math., 150 (1999), 369-454. MR 1726699 (2001d:31004)
  • [KT3] Kenig, C. E., and Toro, T., Poisson kernel characterization of Reifenberg flat chord arc domains, Ann. Sci. École Norm. Sup. (4), 36 (2003), no. 3., 323-401. MR 1977823 (2004d:31010)
  • [KT4] Kenig, C. E., and Toro, T., Free boundary regularity below the continuous threshold: 2-phase problems, J. Reine Angew. Mat., 596 (2006), 1-44. MR 2254803
  • [L] Lavrentiev, M., Boundary problems in the theory of univalent functions, Mat. Sb. (N.S.), 1 (1936), 815-844. English transl. in Amer. Math. Soc. Transl. Ser. 2 32, AMS, 1963, 1-35. MR 0155970 (27:5903)
  • [P1] Pommerenke, C., On univalent functions, Bloch functions and VMOA, Math. Ann., 236 (1978), 199-208. MR 0492206 (58:11352)
  • [P2] Pommerenke, C., Boundary behavior of conformal maps, Springer-Verlag, 1992. MR 1217706 (95b:30008)
  • [R] Reifenberg, E., Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math., 104 (1960), 1-92. MR 0114145 (22:4972)
  • [S1] Semmes, S., Chord arc surfaces with small constant, I, Adv. Math., 85 (1991), 198-223. MR 1093006 (93d:42019a)
  • [S2] Semmes, S., Analysis vs. geometry on a class of rectifiable hypersurfaces in $ {\mathbb{R}}^n$, Indiana Univ. Math. J., 39 (1990), 1005-1035. MR 1087183 (92m:30089)

Review Information:

Reviewer: John B. Garnett
Affiliation: The University of California, Los Angeles
Journal: Bull. Amer. Math. Soc. 45 (2008), 321-327
MSC (2000): Primary 35-02, 31-XX; Secondary 34A26, 35R35, 28A75
Published electronically: July 11, 2007
Review copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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