On the convexity of lemniscates
On the convexity of lemniscates
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{L_1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the lemniscate <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="vertical-bar product Underscript v equals 1 Overscript n Endscripts left-parenthesis z minus zeta Subscript v Baseline right-parenthesis vertical-bar equals 1"> <mml:semantics> <mml:mrow> …