Counterexample to the Lu Qi-Keng conjecture
Counterexample to the Lu Qi-Keng conjecture
There exists a smooth bounded strongly pseudoconvex domain in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper C squared"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">C</mml:mi> </mml:mrow> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{{\mathbf {C}}^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, smoothly equivalent to the ball, whose Bergman kernel function has zeroes.