Codice  QDD 118 
Titolo  Differential 1forms, their integrals ans Potential Theory on the Sierpinski gasket 
Data  20120131 
Autore/i  Cipriani, F.; Guido, D.; Isola, T.; Sauvageot J.L. 
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Abstract  We provide a definition of differential 1forms 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 reconstruction of a 1form from its periods
around lacunas in K; ii) a Hodge decomposition of 1forms with respect to the Hilbertian energy norm; iii) the existence of potentials of elementary 1forms 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 1form. 
