Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...

We use the standard notations: differential forms ap, their exterior algebra A, exterior derivative d<p, Hodge's star operator *, coderivative 3f = (_ 1)nP + n 1*d*(P, Laplace-Beltrami operator A = d3 + Md, exterior product (pAg,, inner product (so,*) = fJmpA*4p, and the Dirichlet norm D(sp) = (dep, dp) + (a<p, 5op). For 0forms u the norm reduces to D(u) = (du, du), and Au has the representation

Consider the operator ?r 2 ?q(), where ?r 2 is the (positive) Laplace-Beltrami operator on a closed manifold of the topological type of the two-sphere S 2 and q is a symmetric non-negative quadratic form in the principal curvatures. Generalizing a well-known theorem of J. Hersch for the Laplace-Beltrami operator alone, it is shown in this note that the second eigenvalue 1 is uniquely maximized,...

Point clouds are becoming ubiquitous thanks to the recent advances in low-cost depth camera hardware. However, many key shape analysis techniques require the availability of a global mesh model and exploit its intrinsic connectivity information. We seek to develop methods for global and local geometric similarity, feature recognition, and segmentation that operate directly on point clouds corre...

We prove uniform weighted high frequency estimates for the resolvent of the Laplace-Beltrami operator on connected infinite volume Riemannian manifolds under some natural assumptions on the metric on the ends of the manifold. This extends previous results by Burq [3] and Vodev [8].

Consider a complete hyperbolic surface which can be partitioned into countably many pairs of pants whose boundary components have lengths less than some constant. We show that any infinite ergodic invariant Radon measure for the horocycle flow is either supported on a a single horocycle associated with a cusp, or corresponds canonically to an extremal positive eigenfunction of the Laplace–Beltr...

We determine the matrix of the balanced metric of the Siegel–Jacobi ball and its inverse. We calculate the scalar curvature, the Ricci form and the Laplace–Beltrami operator of this manifold. We discuss several geometric aspects related with Berezin quantization on the Siegel–Jacobi ball.

We generalize the L spectral cluster bounds of Sogge for the Laplace–Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.