We show that Carathéodory's conjecture on umbilical points of closed convex surfaces may be reformulated in terms of the existence of at least one umbilical point in the graphs of functions f: R 2 → R ...

One of the main theorems of the paper states the following. Let R-K-M be finite extensions of a rational one variable function field R over a finite field of constants. Let S be a finite set of ...