Limit chains on the Sierpinski gasket Michael Hinz 14F4028A8052C9957R9958A10fractalsLaplacianenergydifferential formscell complexes The analysis of the Hodge-Laplacian for differential $p$-forms on smooth Riemannian Manifolds is a well-known theory. The present paper proposes some fractal analog for the case $p = 1$ on the Sierpinski gasket. More precisely, we introduce a new energy functional on substitutes of $1$-forms. It is constructed along a sequence of two-dimensional cell complexes that approximate the Sierpinski gasket 'from above'. The basic techniques resemble ideas known from the analysis of function Laplacians on p.c.f. fractals. We prove the existence of an infinite-dimensional space of limit $1$-chains having positive and finite energy. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4404 10.1512/iumj.2011.60.4404 en Indiana Univ. Math. J. 60 (2011) 1797 - 1830 state-of-the-art mathematics http://iumj.org/access/