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Differential Geometry papers — page 5

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On the Kobayashi-Royden pseudonorm for almost complex manifolds
In this paper we define Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. We prove that…
Boris S. KruglikovAug 25, 1997
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Contact Topology and Hydrodynamics
We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb…
J. Etnyre, R. GhristAug 22, 1997
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On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols
We study various aspects of the noncommutative residue for an algebra of pseudodifferential operators whose symbols have an expansion $a Σj=0∞ am-j, am-j(x,ξ)=Σl=0k…
Matthias LeschAug 13, 1997
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Tree-like curves and their inflection points
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a…
Boris ShapiroAug 12, 1997
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On analytical applications of stable homotopy (the Arnold conjecture, critical points)
We prove the Arnold conjecture for closed symplectic manifolds with π2(M)=0 and M= M. Furthermore, we prove an analog of the Lusternik-Schnirelmann theorem for functions with…
Yuli B. RudyakAug 11, 1997
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On the Lusternik-Schnirelmann category of symplectic manifolds and the Arnold conjecture
We prove that the Lusternik-Schnirelmann category cat(M) of a closed symplectic manifold (M, ω) equals the dimension dim(M) provided that the symplectic cohomology class vanishes on the image…
Yuli B. Rudyak, John OpreaAug 11, 1997
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Pseudo-holomorphic curves and the Weinstein conjecture
We established existence of periodic Reeb orbits for a large class of tight contact structures on closed 3-manifolds, notably the Stein fillable structures, based on a fundamental theorem of Cliff…
Weimin ChenAug 10, 1997
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Exterior differential systems: a geometric approach to PDE. Lecture notes from the 1997 Daewoo workshop
This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To…
J. M. LandsbergAug 8, 1997
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The Symmetries of Solitons
This paper is an expository account of the development of soliton mathematics, from its inception in famous numerical experiments of Fermi-Pasta-Ulam and Zabusky-Kruskal to the recent synthesis of…
Richard S. PalaisAug 8, 1997
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The surfaces capable of division into Infinitesimal Squares by their Curves of Curvature
Classically, isothermic surfaces are characterized as those surfaces which are "divisible into infinitesimal squares by their curvature lines". This characterization is the direct analogue to…
Udo Hertrich-JerominAug 1, 1997
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Yamabe Invariants and Spinc Structures
The Yamabe Invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds,…
Matthew J. Gursky, Claude LeBrunAug 1, 1997
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Geometry via coherent states
It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the…
S. BerceanuAug 1, 1997
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Coherent states, transition amplitudes and embeddings
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for…
S. BerceanuJul 31, 1997
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A remark on Berezin's quantization and cut locus
The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that…
S. BerceanuJul 31, 1997
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Fedosov Manifolds
In this paper we study geometry of symmetric torsion-free connections which preserve a given symplectic form
Israel Gelfand, Vladimir Retakh, M. ShubinJul 30, 1997
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Singular Reduction and Quantization
Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the…
Eckhard Meinrenken, Reyer SjamaarJul 30, 1997
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On the Determinant of One-Dimensional Elliptic Boundary Value Problems
We discuss the ζ-regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.
Matthias Lesch, Jürgen TolksdorfJul 30, 1997
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Lie Group Valued Moment Maps
We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of…
Anton Alekseev, Anton Malkin, Eckhard MeinrenkenJul 26, 1997
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Comparison and Rigidity Theorems in Semi-Riemannian Geometry
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the…
L. Andersson, R. HowardJul 25, 1997
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Fusion of Hamiltonian loop group manifolds and cobordism
We construct an oriented cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties, together with a closed two-form which restricts to the…
Eckhard Meinrenken, Chris WoodwardJul 24, 1997
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Moduli spaces of flat connections on 2-manifolds, cobordism, and Witten's volume formulas
We discuss Witten's formulas for the symplectic volumes of moduli spaces of flat connections on 2-manifolds from the viewpoint of Hamiltonian cobordism as introduced by Ginzburg-Guillemin-Karshon.
Eckhard Meinrenken, Chris WoodwardJul 24, 1997
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Scalar Curvature Rigidity for asymptotically locally hyperbolic manifolds
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The…
L. Andersson, M. DahlJul 24, 1997
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Volumes, middle-dimensional systoles, and Whitehead products
Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of…
Ivan K. Babenko, Mikhail G. Katz, Alexander I. SuciuJul 22, 1997
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A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry
The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature…
L. Andersson, G. J. Galloway, R. HowardJul 22, 1997
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Nonlocal invariants in index theory
This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem…
Steven RosenbergJul 21, 1997
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