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Differential Geometry papers — page 2

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The Positive Fundamental Group of Sp(2) and Sp(4)
In this paper, we examine the homotopy classes of positive loops in Sp(2) and Sp(4). We show that two positive loops are homotopic if and only if they are homotopic through positive loops.
Jennifer SlimowitzDec 2, 1997
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Higher analytic torsion and cohomology of diffeomorphism groups
We consider a closed odd-dimensional oriented manifold M together with an acyclic flat hermitean vector bundle . We form the trivial fibre bundle with fibre M over the manifold of all…
U. BunkeDec 2, 1997
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Existence results for mean field equations
Let Ω be an annulus. We prove that the mean field equation -Δψ=e-βψ∫Ωe-βψ admits a solution with zero boundary for β∈ (-16π,-8π). This is a supercritical case for…
W. Ding, J. Jost, J. Li et al.Nov 30, 1997
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Isometry groups and geodesic foliations of Lorentz manifolds. Part II: Geometry of analytic Lorentz manifolds with large isometry groups
This is Part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in Part I, a compactification of these isometry groups, and called ``bi-polarized'' those…
Abdelghani ZeghibNov 26, 1997
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Poisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/T
We characterize the harmonic forms on a flag manifold K/T defined by Kostant in 1963 in terms of a Poisson structure. Namely, they are ``Poisson harmonic" with respect to the so-called Bruhat…
Sam Evens, Jiang-Hua LuNov 26, 1997
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Relative torsion for representations in finite type Hilbert modules
For a closed manifold equipped with a Riemannian metric, a triangulation, a representation of its fundamental group on an Hilbert module of finite type (over of finite von Neumann algebra), and a…
D. Burghelea, L. Friedlander, T. KappelerNov 25, 1997
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Finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations
We corrected a few errors in the previous submission. These do not affect any of the topological conclusions of the earlier version. We have also included a few observations about the Casson…
Liviu I. NicolaescuNov 24, 1997
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Discrete surfaces of constant mean curvature via dressing
We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the…
Guido HaakNov 21, 1997
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Scattering theory and deformations of asymptotically hyperbolic metrics
For an asymptotically hyperbolic metric on the interior of a compact manifold with boundary, we prove that the resolvent and scattering operators are continuous functions of the metric in the…
David BorthwickNov 20, 1997
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Isometry groups and geodesic foliations of Lorentz manifolds. Part I: Foundations of Lorentz dynamics
This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate…
Abdelghani ZeghibNov 19, 1997
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Kahler geometry of toric varieties and extremal metrics
Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler metrics on (symplectic) toric varieties, using only data on the moment polytope. In this paper,…
Miguel AbreuNov 19, 1997
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Complex Generated by Variational Derivatives. Lagrangian Formalism of Infinite Order and a Generalized Stokes' Formula
We prove that an analog of the exterior differential acts on the space of arbitrary Lagrangians of multidimensional paths on any manifold or supermanifold, thus making this space into a cochain…
Theodore VoronovNov 18, 1997
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Totally geodesic orbits of isometries
We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved…
Fabio Podesta, Luigi VerdianiNov 17, 1997
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Equivariant torsion and G-CW-complexes
For any compact Lie group G we discuss the relation of the equivariant Reidemeister and analytic torsion of G-manifolds with their G-CW structures.
U. BunkeNov 14, 1997
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Morse theory of harmonic forms
We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given…
Michael Farber, Gabriel Katz, Jerome LevineNov 11, 1997
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New examples of conservative systems on S2 possessing an integral cubic in momenta
It has been proved that on 2-dimensional orientable compact manifolds of genus g>1 there is no integrable geodesic flow with an integral polynomial in momenta. There is a conjecture that all…
Elena N. SelivanovaNov 10, 1997
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Critical-exponent Sobolev norms and the slice theorem for the quotient space of connections
The use of certain critical-exponent Sobolev norms is an important feature of methods employed by Taubes to solve the anti-self-dual and similar non-linear elliptic partial differential equations.…
Paul M. N. FeehanNov 9, 1997
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On the localization theorem in equivariant cohomology
We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a…
Michel Brion, Michèle VergneNov 7, 1997
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The moduli space of special Lagrangian submanifolds
This paper considers the natural geometric structure on the moduli space of deformations of a compact special Lagrangian submanifold Ln of a Calabi-Yau manifold. From the work of McLean this is a…
Nigel HitchinNov 4, 1997
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Upper bounds for regularized determinants
Let E be a holomorphic vector bundle on a compact Kähler manifold X. If we fix a metric h on E, we get a Laplace operator Δ acting upon smooth sections of E over X. Using the zeta…
H. Gillet, C. SouléNov 4, 1997
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Mutation and Gauge Theory I: Yang-Mills Invariants
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to…
Daniel RubermanOct 29, 1997
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On the variation of the Poisson structures of certain moduli spaces
Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the…
Johannes HuebschmannOct 29, 1997
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PU(2) Monopoles, I: Regularity, Uhlenbeck Compactness, and Transversality
We prove the existence of perturbations for the PU(2) monopole equations, yielding transversality on the complement of the anti-self-dual or reducible solutions, and the existence of an Uhlenbeck…
Paul M. N. Feehan, Thomas G. LenessOct 29, 1997
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Frobenius Manifolds from Yang-Mills Instantons
We present an elementary self-contained account of semisimple Frobenius manifolds in three dimensions, and exhibit a new family of explicit examples. These examples are constructed from Yang-Mills…
Jan SegertOct 29, 1997
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Classical lifting processes and multiplicative vector fields
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the…
Kirill Mackenzie, Ping XuOct 28, 1997
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