# A properly embedded holomorphic disc in the ball with finite area and dense boundary curve

## Univerza v Ljubljani

I will describe the construction of a properly embedded holomorphic disc in the unit ball of \(\mathbb{C}^2\) having the following surprising combination of properties: - on the one hand, the disc has finite area, and hence is the zero set of a bounded holomorphic function on the ball; - on the other hand, its real analytic boundary curve is everywhere dense in the sphere.