Available in electronic format
Available in print format		 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues: 1891 - Present
Previous Article | Next Article
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

Book Information

Author(s): 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, US$28.00, ISBN 978-0-8218-3920-1

References:

[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)

Additional Information:

Reviewer(s):
John B. Garnett
Affiliation: The University of California, Los Angeles
Email: jbg@math.ucla.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 45 (2008), 321-327.

MSC (2000): Primary 35-02, 31-XX; Secondary 34A26, 35R35, 28A75
DOI: 10.1090/S0273-0979-07-01164-0
PII: S 0273-0979(07)01164-0
Posted: July 11, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google