We study, in this paper, the problem of denoising images/data which are defined over non-flat surfaces. This problem arises often in many medical imaging tasks. The Beltrami flow which was defined in an explicit-intrinsic manner is generalized here to non-flat surfaces and is defined in an implicit way. We formulate the flow in a variational way which is generalized to a scalar field defined ov...

We study the BRST cohomology within a local conformal Lagrangian eld theory model built on a two dimensional Riemann surface with no boundary. We deal with the case of the complex structure parametrized by Beltrami di erential and the scalar matter elds. The computation of all elements of the BRST cohomology is given.

This is an expository article on the question of whether zero lies in the spectrum of the Laplace-Beltrami operator acting on differential forms on a manifold.

Tight Beltrami fields with symmetry. Abstract Given a Seifered fibred 3-manifold M equipped with an S 1-invariant contact form α, we provide a bound on the volume Vol(M) and the curvature, in a suitable adapted Riemannian metric to α, which implies universal tightness of the contact structure ξ = ker α.

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunctions determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete Laplace-Beltrami operator and the discrete Riemannian metric (unique up to a scali...

We address the problem of detecting deformities on elastic surfaces. This is of great importance for shape analysis, with applications such as detecting abnormalities in biological shapes (e.g., brain structures). We propose an effective algorithm to detect abnormal deformations by generating quasi-conformal maps between the original and deformed surfaces. We firstly flatten the 3D surfaces con...

We determine optimal L-properties for the solutions of the general nonlinear elliptic system in the plane of the form fz = H(z, fz), h ∈ L(C), where H is a measurable function satisfying |H(z,w1) − H(z,w2)| ≤ k|w1 − w2| and k is a constant k < 1. We also establish the precise invertibility and spectral properties in L(C) for the operators I − T μ, I − μT, and T − μ, where T is the Beurling tran...