|
A symmetry theorem revisited
Author(s):
John
Lewis;
Andrew
Vogel
Journal:
Proc. Amer. Math. Soc.
130
(2002),
443-451.
MSC (1991):
Primary 31B05, 31B20
Posted:
June 6, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that if harmonic measure and Hausdorff measure are equal on the boundary of certain domains in Euclidean  -space, then these domains are necessarily balls.
References:
-
- [Hel69]
- L. Helms, Introduction to potential theory, Wiley-Interscience, 1969. MR 41:5638
- [KL37]
- M. Keldysh and M. Lavrentiev, Sur la représentation conforme des domain limités par des courbes rectifiables, Ann. Sci. École Norm. Sup. 54 (1937), 1-38.
- [LV]
- John L. Lewis and Andrew L. Vogel, On pseudospheres that are quasispheres, Rev. Mat. Iberoamericana, To appear.
- [LV91]
- John L. Lewis and Andrew L. Vogel, On pseudospheres, Rev. Mat. Iberoamericana 7 (1991), 25-54. MR 92g:31006
- [LV92]
- John L. Lewis and Andrew L. Vogel, On some almost everywhere symmetry theorems, Nonlinear diffusion equations and their equilibrium states, vol. 3, Birkhäuser, 1992, pp. 347-374. MR 93j:35078
- [Mat95]
- P. Mattila, Geometry of sets and measures in euclidean spaces, Cambridge University Press, 1995. MR 96h:28006
- [MMV96]
- P. Mattila, M. S. Melnikov, and J. Verdera, The Cauchy integral, analytic capacity, and uniform rectifiability, Ann. of Math. 144 (1996), 127-136. MR 97k:31004
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
31B05, 31B20
Retrieve articles in all Journals with MSC
(1991):
31B05, 31B20
Additional Information:
John
Lewis
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email:
john@ms.uky.edu
Andrew
Vogel
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
alvogel@syr.edu
DOI:
10.1090/S0002-9939-01-06200-1
PII:
S 0002-9939(01)06200-1
Keywords:
Harmonic measure,
Hausdorff measure,
quasiconformal,
Green's function,
Dirichlet problem
Received by editor(s):
June 20, 2000
Posted:
June 6, 2001
Additional Notes:
The first author was supported in part by an NSF grant
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org