We present a novel approach for computing and solving the Poisson equation over the surface of a mesh. As in previous approaches, we define the Laplace-Beltrami operator by considering the derivatives of functions defined on the mesh. However, in this work, we explore a choice of functions that is decoupled from the tessellation. Specifically, we use basis functions (second-order tensor-product...

In this paper we continue the study of functional calculus for the Laplace{ Beltrami operator on symmetric spaces of the noncompact type begun in 3]; this paper is dedicated to a study of the Poisson semigroup, which we deene shortly. Let G and K be a connected noncompact semisimple Lie group with nite center and a maximal compact subgroup thereof, and consider the symmetric space G=K; also den...

The main goal of the paper is to generalize the Duistermaat-Guillemin trace formula to the case of transversally elliptic operators on a compact foliated manifold. First, let us recall briefly the setting of the classical formula. Let P be a positive self-adjoint elliptic pseudodifferential operator of order one on a closed manifold M (for example, P = √ ∆, where ∆ is the Laplace-Beltrami opera...

Harmonic analysis studies the representation of functions as the linear combination of basic wave-like functions. It plays a fundamental role in the processing of time-series signals and images. Recent years have witnessed many efforts to adapt the Fourier and wavelet analysis to the domain of 3D shapes. The manifold Fourier analysis relies on the eigenfunctions of the Laplace-Beltrami operator...

In this paper we study an extension problem for the Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type and use solution to prove Hardy-type inequalities fractional powers operator. Next, mapping properties last part Poincaré-Sobolev these spaces.

We compute the spectra of Laplace-Beltrami operator, connection Laplacian on 1-forms and Einstein operator symmetric 2-tensors sine-cone over a positive manifold $(M, g)$. conclude under which conditions $(M,g)$, is dynamically stable singular Ricci-de Turck flow rigid as