Valentin Seigneur (ENS de Lyon) : Extending Morse functions from a neighborhood of the sphere to the ball
Consider a smooth function defined in a neighborhood of the unit sphere in some euclidean space. Assume this function has no critical point and that its restriction to the sphere is Morse. Can one extend it to a function defined in the unit ball without critical points? We will discuss this question when the dimension of the sphere is at least 6.