5 papers
Magnitude and diversity of trees
Philippe Bouafia
We compute the magnitude (an isometric invariant of metric spaces) of compact -trees and show that it equals , where denotes the total leng…
Fractional currents and Young geometric integration
Philippe Bouafia
We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by Hölder conti…
Another simple proof of the 1-dimensional flat chain conjecture
Philippe Bouafia, Thierry De Pauw
We provide a short proof of the 1-dimensional flat chain conjecture.
On the exterior product of Hölder differential forms
Philippe Bouafia
We introduce a complex of cochains, -fractional charges (), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cocha…
Non-absolute integration and application to Young geometric integration
Philippe Bouafia
We survey several non-absolutely convergent integrals, including the Henstock-Kurzweil and Pfeffer integrals, and use ideas from these theories to investigate the problem of multid…