[Mini-course] BV functions in Carnot groups | Speaker Dr. Sebastiano Nicolussi Golo, University of Jyväskylä
Speaker: Dr. Sebastiano Nicolussi Golo, University of Jyväskylä (The speaker is currently a visiting scholar at OIST Theoretical Sciences Visiting Program.)
Title: BV functions in Carnot groups
In this lectures I will present the theory of functions of bounded variation (BV functions) in Carnot groups. Carnot groups are Lie groups endowed with a fractal sub-Riemannian metric structure. The exposition will always reference to the classical theory of BV functions on Euclidean spaces (see for instance the monograph by Ambrosio-Fusco-Pallara). In this way, I expect that my lessons will be informative also for those who are familiar neither with BV functions on Euclidean spaces nor with Carnot groups.
In particular, we will study sets of finite perimeter. The structure of sets of finite perimeter is a cornerstone of Geometric Measure Theory. We will see how it (does not yet) extend to Carnot groups.
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