Codice QDD 118 Titolo Differential 1-forms, their integrals ans Potential Theory on the Sierpinski gasket Data 2012-01-31 Autore/i Cipriani, F.; Guido, D.; Isola, T.; Sauvageot J.L. Link Download full text Abstract We provide a definition of differential 1-forms on the Sierpinski gasket K and their integrals on paths. We show how these tools can be used to build up a Potential Theory on K. In particular, we prove: i) a de Rham re-construction of a 1-form from its periods around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of elementary 1-forms on suitable covering spaces of K. We then apply this framework to the topology of the fractal K, showing that each element of the dual of the first Cech homology group is represented by a suitable harmonic 1-form.