Blog

The study of minimal surfaces is one of the central themes in geometric measure theory, and the insights gained from research on the minimal surfaces in particular have had an impact on a wide range of fields of geometry and analysis. Mean curvature flow, which can be considered a time-evolution version of the minimal surface, is a more general problem that also includes minimal surfaces. Compared to the study of minimal surfaces, on the other hand, the amount of research on the mean curvature flow is considerably smaller, and many aspects remain unclear. I will begin by explaining the history of the mean curvature flow in the context of geometric measure theory and Almgren’s works and then introduce the existence and regularity theorem in which I have been involved.

More Information:  https://sites.google.com/view/yoshihirotonegawa/