Geometric Measure Theory and related topics - FIRST WEEK

Contribution List

9. A user’s guide to distributional fractional spaces

Stefani, Giorgio (Università di Padova)

We provide an introduction to the distributional theory of fractional spaces. In the first part of the talk, we define the Riesz fractional gradient, explore its key properties, and introduce the distributional fractional Sobolev and $BV$ spaces along with their main features. In the second part, we discuss the properties of fractional variation and survey recent developments, including the...

10. Besicovitch's 1/2 problem

Massaccesi, Annalisa (Università di Padova)

Besicovitch's problem

Besicovitch's problem investigates the smallest threshold guaranteeing rectifiability for a set with Hausdorff -dimensional finite measure when the lower density of the set is larger than almost everywhere. Besicovitch conjectured that (hence the name of the problem) and proved , then Preiss and Tišer improved the bound to . In a recent work in...

6. On the de Rham complex in Carnot groups

Tripaldi, Francesca (University of Leeds)

Carnot groups are a class of nilpotent Lie groups naturally equipped with a horizontal distribution. When endowed with a compatible metric, they form subRiemannian manifolds, which are central objects in non-holonomic systems and control theory.
To better capture the algebraic and geometric structure of such spaces, Rumin introduced a refinement of the de Rham complex, now known as the Rumin...

7. Quantitative differentiability and rectifiability

Young, Robert (New York University)

8. Regularity for area minimizing integral currents

Resende, Reinaldo (Carnegie Mellon University)

We will explore the state of the art in interior and boundary regularity for solutions of the oriented Plateau problem, specifically in the framework of integral currents. After reviewing recent developments in interior regularity, we will shift our focus to the boundary setting. In this context, we will discuss the types of boundary points that naturally arise in the theory and introduce...

11. The Plateau problem for wet films

Prof. Maggi, Francesco (University of Texas at Austin)