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math.MG2020
Another point of view on Kusuoka's measure
Ugo Bessi
Kusuoka's measure on fractals is a Gibbs measure of a very special kind, because its potential is discontinuous, while the standard theory of Gibbs measures requires continuous (ac…
math.MG2020
Cheeger's energy on the Harmonic Sierpinski Gasket
Ugo Bessi
Koskela and Zhou have proven that, on the harmonic Sierpinski gasket with Kusuoka's measure, the "natural" Dirichlet form coincides with Cheeger's energy. We give a different proof…
math.OC2020
Hamilton-Jacobi in metric spaces with a homological term
Ugo Bessi
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilto…