Applying a theorem due to Belopol’ski and Birman, we show that the Laplace-Beltrami operator on 1-forms on R endowed with an asymptotically Euclidean metric has absolutely continuous spectrum equal to [0,+∞).

We adapt in the present note the perturbation method introduced in [3] to get a lower Gaussian bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.

In existing anisotropic diffusion-based semi-supervised learning approaches, anisotropic graph Laplacian is estimated based on (potentially noisy) function evaluations. We propose to regularize the graph Laplacian estimates. We develop a framework that regularizes the Laplace-Beltrami operators on Riemannian manifolds, and discretize it to a regularizer on diffusivity operators on graphs. Isotr...

Let $\Delta_{g}$ be the Laplace Beltrami operator on a manifold $M$ with Dirichlet (resp.,Neumann) boundary conditions. We compare spectrum of Riemannian for Neumann condition and . Then we construct aneffective method obtaining small eigenvalues Neumann's problem.

The spectrum and the eigenbasis of the Laplace–Beltrami operator on the suspensions of toric automorphisms are investigated. A description in terms of solutions of one-dimensional Schrödinger’s equation is presented. Bibliography: 10 titles. §

We present an algorithm for approximating the Laplace-Beltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the d-dimensional space. We show that this PCD Laplace (Point-Cloud Data Laplace) operator converges to the Laplace-Beltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that ...

The Laplace-Beltrami operator is an extension of the Laplacian from flat domains to curved manifolds. It was proven to be useful for color image processing as it models a meaningful coupling between the color channels. This coupling is naturally expressed in the Beltrami framework in which a color image is regarded as a two dimensional manifold embedded in a hybrid, five-dimensional, spatial-ch...

The Laplace-Beltrami operator is an extension of the Laplacian from flat domains to curved manifolds. It was proven to be useful for color image processing as it models a meaningful coupling between the color channels. This coupling is naturally expressed in the Beltrami framework in which a color image is regarded as a two dimensional manifold embedded in a hybrid, five dimensional, spatial-ch...