Guy R. P. David

He is mainly concerned with geometric measure theory and its connection with other parts of mathematical analysis. Geometric measure theory deals with mild regularity properties of sets in Euclidean space. Quantitative aspects of this are useful for example in the study of operators given by integration against a singular kernel (are they bounded?), analytic capacity (how to decide on which open subsets of the plane there are nonconstant analytic functions), or (more traditionally) calculus of variations (how regular are functions or sets that minimize a functional, like the Mumford-Shah functional).