The Brennan conjecture is a conjecture in complex analysis estimating the integral powers of the moduli of the derivatives of conformal maps of a simply connected open subset of the complex plane onto the open unit disk. It was formulated by James E. Brennan in 1978; Brennan proved a partial range himself and Bertilsson extended it in 1999, but the full result remains open. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementFor a conformal map phi of a simply connected open subset W of the complex plane, with at least two boundary points in the extended complex plane, onto the open unit disk, the integral over W of |phi'|^p dx dy is finite whenever 4/3 < p < 4. 1 Proposed Year Progress Toward ResolutionBrennan proved the result for 4/3 < p < p0 for some constant p0 > 3, and Bertilsson proved in 1999 that it holds for 4/3 < p < 3.422; the full result remains open. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
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Source Brennan Conjecture (Wikipedia)
Sources
1. Brennan Conjecture (Wikipedia)
Wikimedia FoundationLead section
The conjecture was formulated by James E. Brennan in 1978.
Lead section, opening sentence
In mathematics, specifically complex analysis, the Brennan conjecture is a conjecture estimating (under specified conditions) the integral powers of the moduli of the derivatives of conformal maps into the open unit disk.
Second paragraph
but the full result remains open.
In Branch: Complex Analysis, Lead sentence
In mathematics, specifically complex analysis, the Brennan conjecture is a conjecture estimating (under specified conditions) the
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