A survey on Bernstein-type theorems for complete graphical surfaces
Authors: Yu Kawakami
Summary: We survey Bernstein-type theorems of graphical surfaces within the Euclidean area and the Lorentz-Minkowski area. Extra particularly, we clarify a number of proofs of the Bernstein theorem for minimal graphs within the Euclidean 3-space. Moreover, we present the Heinz-type imply curvature estimates for graphs within the Euclidean 3-space and space-like graphs within the Lorentz-Minkowski 3-space. As an software of those estimates, we give Bernstein-type theorems for fixed imply curvature graphs within the Euclidean 3-space and fixed imply curvature space-like graphs within the Lorentz-Minkowski 3-space, respectively. We additionally research Bernstein-type outcomes for minimal graphs within the Euclidean 4-space and the Calabi-Bernstein theorem within the Lorentz-Minkowski 3-space.
