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Bloch functions, asymptotic variance, and zero packing | | Haakan Hedenmalm
; | | Date: |
10 Feb 2016 | | Abstract: | We study a new type of extremal problem in complex analysis, referred to as
"zero packing". We relate the corresponding minimal discrepancy density with
the asymptotic variance for Bloch functions of the form "Bergman projection of
bounded functions" and obtain a corresponding identity. Together with related
work of Ivrii, this gives the asymptotic behavior of the universal
quasiconformal integral means spectrum for small values of quasiconformality k
and small exponents t. In particular, the conjectured behavior is shown to be
smaller than conjectured by Prause and Smirnov, which also shows that there are
no quasidisks with dimension 1+k^2, at least for small k. | | Source: | arXiv, 1602.3358 | | Services: | Forum | Review | PDF | Favorites | |
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