Miruna-Stefana Sorea, Max-Planck-Institut für Mathematik in den Naturwissenschaften, The shapes of level curves of real polynomials near strict local minima
ZoomWe consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries…