Geometric Hodge Star Operator with Applications to the Theorems of Gauss and Green

requires that a normal vector field n(p) be defined a.e. p ∈ ∂A. In this paper we give a new proof and extension of this theorem by replacing n with a limit ⋆∂A of 1-dimensional polyhedral chains taken with respect to a norm. The operator ⋆ is a geometric dual to the Hodge star operator and is defined on a large class of k-dimensional domains of integration A in n-space the author calls chainlets. Chainlets include a broad range of domains, from smooth manifolds to soap bubbles and fractals. We prove as our main result the Star theorem