The Brennan conjecture is a mathematical hypothesis (in complex analysis) for estimating (under specified conditions) the integral powers of the moduli of the derivatives of conformal maps into the open unit disk. The conjecture was formulated by James E. Brennan in 1978.
Let W be a simply connected open subset of formula_1 with at least two boundary points in the extended complex plane. Let formula_2 be a conformal map of W onto the open unit disk. The Brennan conjecture states that
formula_3 whenever formula_4. Brennan proved the result when formula_5 for some constant formula_6. Bertilsson proved in 1999 that the result holds when formula_7, but the full result remains open.
References.
 ;templatestyles src="Reflist/styles.css" / ;