Mathematics Colloquium

An evolving surface is a mean curvature flow if the normal component of its velocity field is given by the mean curvature (the sum of the principal curvatures); equivalently, a mean curvature flow is a steepest descent  or (negative) gradient flow trajectory for the area functional.  First introduced in the physics literature in the 1950s, the mean curvature flow equation has been studied intensely by mathematicians since the 1970s with the aim of understanding singularity formation and developing a rigorous mathematical treatment of flow through singularities.   Rapid progress in the last few years has led to the solution of several longstanding conjectures, and laid the groundwork for the solution of other conjectures which seemed untractable just a few years ago.  

 

After covering general background, the lecture will review some central issues and previous work, before describing the recent developments.