Let χλ (cf (1.1)) be the unit spectral projection operator with respect to the Laplace-Beltrami operator ∆ on a closed Riemannian manifold M . We generalize the (L2, L∞) estimate of χλ by Hörmander [3] to those of covariant derivatives of χλ Moreover we extend the (L2, Lp) estimates of χλ by Sogge [7] [8] to (L2, Sobolev Lp) estimates of χλ.

We establish various Lp estimates for the Schrödinger operator −∆ + V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where ∆ is the Laplace-Beltrami operator and V belongs to a reverse Hölder class. At the end of this paper we apply our result on Lie groups with polynomial growth.

The physical situation which has initiated this research is that of a dielectric particle with electric charges on its surface, placed in electric field. Here, the diffusion equation of the charges is coupled with the Maxwell equations. There is an analytical solution of this system of equation [1] which involves some functional calculus with operators, in particular with Laplace-Beltrami opera...

Shape analysis plays a pivotal role in a large number of applications, ranging from traditional geometry processing to more recent 3D content management. In this scenario, spectral methods are extremely promising as they provide a natural library of tools for shape analysis, intrinsically defined by the shape itself. In particular, the eigenfunctions of the Laplace-Beltrami operator yield a set...

This paper concerns G-invariant systems of second order differential operators on irreducible Hermitian symmetric spaces G/K. The systems of type (1, 1) are obtained from K-invariant subspaces of p+ ⊗ p−. We show that all such systems can be derived from a decomposition p+ ⊗ p− = H′ ⊕ L ⊕ Hc. Here L gives the Laplace-Beltrami operator and H = H′⊕L is the celebrated Hua system, which has been ex...

We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace-Beltrami operator on M . Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion. 2000 Mathematics Subject Classification. Primary 58J65, 53C21.

An intrinsic discrete Laplace-Beltrami operator on simplicial surfaces S proposed in [2] was established via an intrinsic Delaunay tessellation on S. Up to now, this intrinsic Delaunay tessellations can only be computed by an edge flipping algorithm without any provable complexity analysis. In the paper, we show that the intrinsic Delaunay triangulation can be obtained from a duality of geodesi...