zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Convexity of harmonic densities. (English) Zbl 1253.31004
Summary: The convexity of the densities of harmonic measures is proven for subsets of a circle or of the real line. As a consequence, we get the convexity of the densities of equilibrium measures for compact sets lying on circles or the real axis.

31A15Potentials and capacity, harmonic measure, extremal length (two-dimensional)
Full Text: DOI
[1] Ancona, A.: Démonstration d’une conjecture sur la capacité et l’effilement. C. R. Acad. Sci. Paris S` er. I Math. 297 (1983), no. 7, 393-395. · Zbl 0544.31006
[2] Benko, D., Damelin, S. B. and Dragnev, P. D.: On supports of equilibrium measures with concave signed equilibria. J. Comput. Anal. Appl. 14 (2012), no. 4, 752-766. · Zbl 1255.31001
[3] Benko, D. and Dragnev, P. D.: Balayage ping pong: A convexity of equilibrium measures. Constr. Approx. 36 (2012), no. 2, 191-214. · Zbl 1250.31003 · doi:10.1007/s00365-011-9143-x
[4] Garnett, J. B. and Marshall, D. E.: Harmonic measure. New Mathematical Monographs 2, Cambridge University Press, Cambridge, 2005. · Zbl 1077.31001
[5] Landkof, N. S.: Foundations of modern potential theory. Grundlehren der mathe- matischen Wissenschaften 180, Springer-Verlag, New York-Heidelberg, 1972.
[6] Ransford, T.: Potential theory in the complex plane. Cambridge University Press, Cambridge, 1995. · Zbl 0828.31001
[7] Simon, B.: Orthogonal polynomials on the unit circle, Part 2, Spectral theory. Amer- ican Mathematical Society Colloquium Publications 54, part 2, American Mathemat- ical Society, Providence, RI, 2005. · Zbl 1082.42021