Sofia Ortega Castillo

Strong pseudoconvexity in Banach spaces

I will talk about strong pseudoconvexity as a relevant notion to understand the local geometry of domains of holomorphy with C² boundary in the finite-dimensional Euclidean spaces over the complex plane. It is also desirable to comprehend the geometry near the boundary of domains of holomorphy in arbitrary Banach spaces, but it may be out of reach to have two degrees of differentiability of a simple example such as the ball of a Banach space, because its norm may lack differentiability. I will justify a suitable notion of strong pseudoconvexity for bounded domains without C²-smooth boundary, that will rely on an adequate generalization of a strict plurisubharmonic function to the case when it is not differentiable. I will also mention examples for this extended notions.