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

To any compact Riemannian manifold (M, g) (with or without boundary), we can associate a second-order partial differential operator, the Laplace operator ∆, defined by ∆(f) = −div(grad(f)) for f ∈ L(M, g). We will also sometimes write ∆g for ∆ if we want to emphasize which metric the Laplace operator is associated with. The set of eigenvalues of ∆ (the spectrum of ∆, or of M), which we will wri...

In the applications of the method of fundamental solutions, locations of sources are treated either as variables or a priori known constants. In which, the former results in a nonlinear optimization problem and the other has to face the problem of locating sources. Theoretically, farther sources results in worse conditioning and better accuracy. In this paper, a practical procedure is provided ...

The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...

The spectral determinant of the Schrödinger operator (−∆+V (x)) on a graph is computed for general boundary conditions. (∆ is the Laplacian and V (x) is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

We consider the p-Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p →∞.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit problem as p → 1.

This work concerns the multi-point nonlinear Neumann boundaryvalue problem involving a p-Laplacian-like operator (φ(u′))′ = f(t, u, u′), t ∈ (0, 1), u′(0) = u′(η), φ(u′(1)) = m X

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry. © 2010 Elsevier Inc. All rights reserved.

We study regularity of mild and strong solutions for an abstract mathematical model of a flexible space structure under appropriate initial conditions. We apply our results showing qualitative properties of the trajectories in case of the negative Laplacian operator.