The Harmonic Operator for Exterior Differential Forms

The Harmonic Operator for Exterior 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 ...

The Dirichlet to Neumann mapping for harmonic differential forms

We show that the full symbol of the Dirichlet to Neumann map of the k-form Laplace’s equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series of the metric at the boundary. This extends the result of Lee and Uhlmann for the case k = 0. The proof avoids the computation of the full symbol by using the calculus of pseudo-differential operators...

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...

Graph Braid Groups Exterior Face Algebras and Differential Forms

I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, lo...