The Higher Spin Laplace Operator

Eigenfunctions of the Laplace operator

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

Adaptive Discrete Laplace Operator

Diffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, generalizing the operator defined on meshes. We study its eigen...

The Laplace operator is essentially self-adjoint

Quasiregular mappings and the p-Laplace operator

We describe the role of p-harmonic functions in the theory of quasiregular mappings.

Commutative Rule involving the Laplace Operator

Commutation rules between the Laplace operator and other basic operators (include the divergence, the curl, and the gradient operator) are established. These rules were seldom noticed in the past. However, it is shown that they lead to an alternative derivation of the electromagnetic fields due to an arbitrary current distribution in a homogeneous environment without referring to the vector pot...