Champagne subdomains with unavoidable bubbles

Hansen W, Netuka I (2013)
Advances In Mathematics 244: 106-116.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
A champagne subdomain of a connected open set U not equal empty set in R-d, d >= 2, is obtained by omitting pairwise disjoint closed balls (B) over bar (x, r(x)), x is an element of X, the bubbles, where X is an infinite, locally finite set in U. The union A of these balls may be unavoidable, that is, Brownian motion, starting in U \ A and killed when leaving U, may hit A almost surely or, equivalently, A may have harmonic measure 1 for U \ A. Recent publications by Gardiner and Ghergu (d >= 3) and by Pres (d = 2) give rather sharp answers to the question of how small such a set A may be, when U is the unit ball. In this paper, using a totally different approach, optimal results are obtained, which hold also for arbitrary connected open sets U. (C) 2013 Elsevier Inc. All rights reserved.
Stichworte
Brownian motion; Harmonic measure; Capacity; Champagne subregion; Unavoidable bubbles; Champagne subdomain
Erscheinungsjahr
2013
Zeitschriftentitel
Advances In Mathematics
Band
244
Seite(n)
106-116
ISSN
0001-8708
Page URI
https://pub.uni-bielefeld.de/record/2622128

Zitieren

Hansen W, Netuka I. Champagne subdomains with unavoidable bubbles. Advances In Mathematics. 2013;244:106-116.
Hansen, W., & Netuka, I. (2013). Champagne subdomains with unavoidable bubbles. Advances In Mathematics, 244, 106-116. doi:10.1016/j.aim.2013.05.011
Hansen, W., and Netuka, I. (2013). Champagne subdomains with unavoidable bubbles. Advances In Mathematics 244, 106-116.
Hansen, W., & Netuka, I., 2013. Champagne subdomains with unavoidable bubbles. Advances In Mathematics, 244, p 106-116.
W. Hansen and I. Netuka, “Champagne subdomains with unavoidable bubbles”, Advances In Mathematics, vol. 244, 2013, pp. 106-116.
Hansen, W., Netuka, I.: Champagne subdomains with unavoidable bubbles. Advances In Mathematics. 244, 106-116 (2013).
Hansen, Wolfhard, and Netuka, Ivan. “Champagne subdomains with unavoidable bubbles”. Advances In Mathematics 244 (2013): 106-116.

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