A Bernstein-type theorem for two-valued minimal graphs in dimension four

Abstract: The Bernstein theorem is a classical result for minimal graphs. It states that a globally defined solution of the minimal surface equation on $\mathbb{R}^n$ must be linear, provided the dimension is small enough. We present an analogous theorem for two-valued minimal graphs, valid in dimension four. By definition two-valued functions take values in the unordered pairs of real numbers; they arise as the local model of branch point singularities. The plan is to juxtapose this with the classical single-valued theory, and explain where some of the difficulties emerge in the two-valued setting.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar