Operator Calculus of Differential Chains and Differential Forms

Caratheodory operator of differential forms

* Correspondence: tzymath@gmail. com Department of Mathematics and System Science, National University of Defense Technology, Changsha, PR China Abstract This article is devoted to extensions of some existing results about the Caratheodory operator from the function sense to the differential form situation. Similarly as the function sense, we obtain the convergence of sequences of differential ...

Differential Forms in Geometric Calculus

Geometric calculus and the calculus of differential forms have common origins in Grassmann algebra but different lines of historical development, so mathematicians have been slow to recognize that they belong together in a single mathematical system. This paper reviews the rationale for embedding differential forms in the more comprehensive system of Geometric Calculus. The most significant app...

Calculus of Variations for Differential Forms

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of the type, ∫

Dirichlet to Neumann Operator on Differential Forms

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN...

The Harmonic Operator for Exterior Differential Forms.