The Bernstein's Problem

This course aims to introduce to the Berstein problem and to its generalizations. The "Bernstein problem" is the question whether minimal hypersurfaces in R^{n+1} which can globally be written as a graph must necessarily be Euclidean hyperplanes. Its complete solution (a positive answer if and only if n < 8) is a cornerstone in the development of Geometric Measure Theory and Geometric Analysis, and fits into a line of research that recently received new impulse, with the solution to a longstanding open problem (at least, in some of the conjectured ambient dimensions). The aim of the course is to discuss the original Bernstein problem and its proofs, and to some of the recent approaches to the more general problem of characterizing complete, stable minimal hypersurfaces (the "stable Bernstein problem").