國立清華大學 數學系

Abstract:
Although smooth objects are most desired by mathematicians, in many situations singularities are unavoidable. In the case of minimal hypersurfaces the presence of singularities is expected at certain dimensions. However, we are able to control the size of the singular set. In order to construct smooth minimal hypersurfaces it is important to understand the singular ones as they provide a model for how these hypersurfaces may degenerate.

We will discuss estimates on the size of singular set of minimal hypersurfaces and generalizations of such estimates to other variational problems. If time permits we will address the problem of constructing singular objects and some open problems.