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Surface Evolution Under Curvature Flows
(Elsevier, 2002)
In many areas of computer vision, such as multiscale analysis and shape description, an image or surface is smoothed by a nonlinear parabolic partial differential equation to eliminate noise and to reveal the large global ...
Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers
(Elsevier, 2002)
In this paper we study the characteristic polynomials \(S(x)=\det(xI−F| II_{p,q})\) of automorphisms of even unimodular lattices with signature \((p,q)\). In particular, we show that any Salem polynomial of degree \(2n\) ...
Coxeter Groups, Salem Numbers and the Hilbert Metric
(Springer Verlag, 2002)
The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology
(Elsevier, 2002)
Let M be a connected, compact, orientable 3-manifold with \(b_1(M)>1\), whose boundary (if any) is a union of tori. Our main result is the inequality \({\parallel \phi \parallel}_A \le {\parallel \phi \parallel}_T\) between ...
Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
(Walter de Gruyter, 2002)
This paper presents the first examples of K3 surface automorphisms \(f : X \rightarrow X\) with Siegel disks (domains on which f acts by an irrational rotation). The set of such examples is countable, and the surface \(X\) ...
Relaxation of excited states in nonlinear Schrödinger equations
(Oxford University Press (OUP), 2002)
We consider a nonlinear Schrödinger equation with a bounded local potential in ℝ3. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial ...
Stable Directions for Excited States of Nonlinear Schrödinger Equations
(Informa UK Limited, 2002)
We consider nonlinear Schrödinger equations in R3. Assume that the linear Hamiltonians have two bound states. For certain finite codimension subset in the space of initial data, we construct solutions converging to the ...
Some Recent Transcendental Techniques in Algebraic and Complex Geometry
(International Congress of Mathematicians, 2002)
This article discusses the recent transcendental techniques used in the proofs of the following three conjectures. (1) The plurigenera of a compact projective algebraic manifold are invariant under holomorphic deformation. ...
Higher nimbers in pawn endgames on large chessboards
(Cambridge University Press, 2002)
We answer a question posed in [Elkies 1996] by constructing a class of pawn endgames on mXn boards that show the Nimbers <i>*k</i> for many large <k>k</k>. We do this by modifying and generalizing T.R. Dawson’s “pawns game” ...