Geometric Analysis Seminar

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

"Bounds on total curvature and the Bernstein's problem in dimension 2, Part II"

After completing the proof of the monotonicity formula, we will define the notion of density of a minimal submanifold and prove some properties of the density function. We will recall some basic properties of the Gauss map followed by the logarithmic cutoff trick and will then use the latter to get a bound on the total curvature of a minimal graph in $\mathbb{R}^3$. As a corollary, we will give a short and elegant proof of the Bernstein's problem in dimension 2.

M3 3103