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- W1753274081 abstract "A champagne subregion of a connected open set $Uneemptyset$ in $R^d$, $dge 2$, is obtained omitting pairwise disjoint closed balls $bar B(x, r_x)$, $xin X$, the bubbles, where $X$ is a locally finite set in $U$. The union $A$ of these balls may be unavoidable, that is, Brownian motion, starting in $Usetminus A$ and killed when leaving $U$, may hit $A$ almost surely or, equivalently, $A$ may have harmonic measure one for $Usetminus A$. Recent publications by Gardiner/Ghergu ($dge 3$) and by Pres ($d=2$) give rather sharp answers to the question how small such a set $A$ may be, when $U$ is the unit ball. In this paper, using a new criterion for unavoidable sets and a straightforward approach, much stronger results are obtained, results which hold as well for an arbitrary open set $U$." @default.
- W1753274081 created "2016-06-24" @default.
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- W1753274081 date "2012-06-07" @default.
- W1753274081 modified "2023-09-27" @default.
- W1753274081 title "Champagne subregions with unavoidable bubbles" @default.
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