EVENTI
Given a perimeter functional P in a measure space (X, m), the Cheeger problem relative to an m-measurable set Ω ⊂ X consists in minimizing the quotient P(E)/m(E) among all m-measurable sets E ⊂ Ω such that m(E) ∈ (0,∞) and P(E) < ∞. During the last 50 years, the Cheeger problem has been extensively studied and generalized in several directions in view of its numerous applications.
We will present a general approach to the Cheeger problem, obtained in a recent collaboration with Franceschi, Pinamonti and Saracco, requiring minimal assumptions on the ambient space and the perimeter functional. We will then discuss some applications of our results to three particular settings: the distributional fractional variation, introduced in a long-standing project with Comi, the non-local K-perimeter, studied in collaboration with Bessas, and minimal partition problems, following a recent joint work with Saracco.
Ref. Dott. S. Cito e A. Carbotti