Harmonic measure of radial line segments and symmetrization

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Let lk = {z : arg z = αk, r1 ≤ |z\ ≤ r2} for k = 1, . . ., n, 0 < r1 < r2 ≤ 1, and αk ∈ ℝ; let E = Unk=1 lk; let E* = {z : arg zn = 0, r1 ≤ |z| ≤ r2}; and let ωE(z) be the harmonic measure of E with respect to the domain {z : \z\ <1} \ E. The inequality ωE(0) ≤ ωE* (0), is established, which solves the problem of Gonchar on the harmonic measure of radial slits. The proof uses the dissymmetrization method of Dubinin and the method of the extremal metric in the form of the problem of extremal partitioning into non-overlapping domains.

Original languageEnglish
Pages (from-to)1701-1718
Number of pages18
JournalSbornik Mathematics
Issue number11-12
StatePublished - 1998


Dive into the research topics of 'Harmonic measure of radial line segments and symmetrization'. Together they form a unique fingerprint.

Cite this