Abstract for the talk on 19.01.2016 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Ludek Zajicek (Karls-Universität Prag)
Properties and applications of DC functions
A function in ℝn is called DC (d.c., delta-convex) if it is the difference of two continous functions f1, f2 (i.e., f = f1 − f2). DC functions are a natural and important joint generalization of both C2 smooth and convex functions. I will recall some properties of DC functions and will give some information on several (older and quite recent) their applications: a) to singularities of convex functions; b) to “distance spheres” in Riemann spaces and in convex surfaces; c) to the theory of curvature measures of non-regular sets. Several open questions will be presented.