Daniel Grieser

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Let (Gε)ε>0 be a family of ’ε-thin’ Riemannian manifolds modeled on a finite metric graph G, for example, the ε-neighborhood of an embedding of G in some Euclidean space with straight edges. We study the asymptotic behavior of the spectrum of the Laplace-Beltrami operator on Gε as ε → 0, for various boundary conditions. We obtain complete asymptotic(More)
We discuss aspects of the L–Stokes theorem on certain manifolds with singularities. We show that the L–Stokes theorem does not hold on real projective varietes, even for isolated singularities. For a complex projective variety of complex dimension n, with isolated singularities, we show that the Laplacians of the de Rham and Dolbeault complexes are discrete(More)
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior of a manifold with boundary, where the boundary has the structure of a tower of fibre bundles. The class of operators(More)
A thin tube is an n-dimensional space which is very thin in n−1 directions, compared to the remaining direction, for example the ε-neighborhood of a curve or an embedded graph in Rn for small ε. The Laplacian on thin tubes and related operators have been studied in various contexts, with different goals but overlapping techniques. In this survey we explain(More)
Access to security spaces and the verification of credit cards require, ideally, a simple and inexpensive system that combines accuracy with a high resistance to compromise. We have been investigating such a system. This system incorporates a novel fingerprint input arrangement that permits the use of optical pattern recognition for fingerprint verification(More)
We show how ’test’ vector fields may be used to give lower bounds for the Cheeger constant of a Euclidean domain (or Riemannian manifold with boundary), and hence for the lowest eigenvalue of the Dirichlet Laplacian on the domain. Also, we show that a continuous version of the classical Max Flow Min Cut Theorem for networks implies that Cheeger’s constant(More)
A partition n = {A,, . . . . A,) of the set [n] = { 1, . . . . n} is an (unordered) family of nonempty subsets A,, . . . . A, of [n] which are pairwise disjoint and whose union is [n]. We call the Ai the blocks of rc, and let 1x1 =m. A partition {B,, . . . . B,} is a refinement of {A,, . . . . A,} if each Bj lies in some Ai. It is well known (but of no(More)
A pattern recognition system that uses incoherent spatial filtering to recognize images directly from a narrowband phosphor television monitor is described. Images of real objects are captured with a television camera. These images are then edge-enhanced electronically and displayed on the TV monitor. The monitor output is used directly as the input to a(More)