On nonconvexity of graphs of polynomials of several real variables
To every nonempty closed subset of a Banach space a measure of nonconvexity is associated. It is proved, that a suitable estimate of nonconvexity of graphs of continuous functions over all lines induces a nice estimate of the nonconvexity of graphs of the entire functions. Such result implies the existence of continuous selections for multifunctions the values of which are graphs of the considered functions. Positive results for quadratic forms and negative ones for cubics are provided. The proofs are geometrical in nature and the paper contains 9 pictures.
scientific article; zbMATH DE number 1230457