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Saturday, May 16, 2020 | History

7 edition of The hypoelliptic Laplacian and Ray-Singer metrics found in the catalog.

The hypoelliptic Laplacian and Ray-Singer metrics

by Jean-Michel Bismut

  • 361 Want to read
  • 26 Currently reading

Published by Princeton Univeristy Press in Princeton, NJ .
Written in English

    Subjects:
  • Differential equations, Hypoelliptic,
  • Laplacian operator,
  • Metric spaces

  • Edition Notes

    Includes bibliographical references and index.

    StatementJean-Michel Bismut, Gilles Lebeau.
    ContributionsLebeau, Gilles.
    Classifications
    LC ClassificationsQA377 .B674 2008
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL16659577M
    ISBN 109780691137315, 9780691137322
    LC Control Number2008062103

    Ray Jean: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. Jean-Michel Bismut (born 26 February ) is a French mathematician who has been a Professor at the Université Paris-Sud since His mathematical career covers two apparently different branches of mathematics: probability theory and differential mater: Ecole Polytechnique.

      The Hypoelliptic Laplacian and Ray-Singer Metrics. (Annals of Mathematics Studies, vol. ). VIII, pp. Princeton University Press, Princeton, EUR The purpose of this book is to develop the analytic theory of the hypoelliptic Laplacian and to establish corresponding results on the associated Ray-Singer analytic torsion. Many details can be found in Montgomery’s book [38]. To define the intrinsic hypoelliptic Laplacian, we proceed as in Riemannian geometry. In Riemannian geometry the invariant Laplacian (called the Laplace–Beltrami operator) is defined as the divergence of the gradient where the gradient is obtained via the Riemannian metric and.

    The various contributions in this volume cover a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kähler geometry, index theory, and hypoelliptic Laplacian and analytic torsion. The book includes papers on the most recent advances as well as survey articles on new developments. The hypoelliptic Laplacian. The hypoelliptic Laplacian and Ray-Singer metrics, volume of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, J.-M. Bismut. Loop spaces and the hypoelliptic Laplacian. In his book "Growth and Forms", first published in , d’Arcy Thompson, a Scottish naturalist and.


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The hypoelliptic Laplacian and Ray-Singer metrics by Jean-Michel Bismut Download PDF EPUB FB2

The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic by: Introduction (pp.

) The purpose of this book is to develop the analytic theory of the hypoelliptic Laplacian and to establish corresponding results on the associated Ray-Singer analytic torsion. We also introduce the corresponding theory for families of hypoelliptic Laplacians, and we construct the associated analytic torsion forms.

The hypoelliptic Laplacian and Ray-Singer metrics. [Jean-Michel Bismut; Gilles Lebeau] -- This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is.

The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a.

The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.

The Hypoelliptic Laplacian and Ray-Singer Metrics 在线试读 This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow.

The secondary classes for two metrics 22 Determinant bundle and Ray-Singer metric 23 Chapter 2. The hypoelliptic Laplacian on the cotangent bundle 25 • A deformation of Hodge theory 25 The hypoelliptic Weitzenbock formulas 29 Hypoelliptic Laplacian and standard Laplacian 30 A deformation of Hodge theory in families The Hypoelliptic Laplacian and Ray-Singer Metrics Presents the analytic foundations to the theory of the Hypoelliptic Laplacian.

This book shows that the Hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. It gives the proper functional analytic setting in order to study this operator and develop a.

The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.5/5(1).

The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM) Series:Annals of Mathematics Studies The hypoelliptic Laplacian on the cotangent bundle. Pages Get Access to Full Text. Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics.

Pages The hypoelliptic Laplacian Jean-Michel Bismut (Orsay) The hypoelliptic Laplacian and Ray-Singer metrics. to appear, [7] J.-M.

Bismut and W. Zhang. An extension of a theorem by Cheeger and M uller. Ast erisque, (), With an appendix by Fran˘cois Laudenbach. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in.

Jean-Michel Bismut and Gilles Lebeau, The hypoelliptic Laplacian and Ray-Singer metrics, Annals of Mathematics Studies, vol. Princeton University Press, Princeton, NJ, MR ; Jean-Michel Bismut, A survey of the hypoelliptic Laplacian, Astérisque (), 39–69 (English, with English and French summaries).

Géométrie Cited by: 3. In our proof we do not use the fact that the hypoelliptic Laplacian deforms the elliptic Laplacian. Hypoelliptic Laplacian and hypoelliptic Ray–Singer metric. We use the notation in the Introduction. Let π: X ⁎ → X be the canonical projection. We denote by p ∈ C ∞ (X ⁎, π ⁎ (T ⁎ X)) the tautological by: 5.

One tool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for the deformation.

The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Find in a Library Find The Hypoelliptic Laplacian and Ray-Singer Metrics.(AM) near you. J.-M. Bismut, G. LebeauThe Hypoelliptic Laplacian and Ray–Singer Metrics Annals of Mathematics Studies, vol.Princeton University Press, Princeton, NJ, USA () Google ScholarCited by: 1.

Abstract. In recents works, J.-M. Bismut has introduced an “hypoelliptic Laplacian” acting on differentials forms on the cotangent bundle T*X of a Riemannian compact manifold operator is a deformation of the Hodge Laplacian on present here some analytic properties of this new : Gilles Lebeau.

We define hypoelliptic Quillen metrics, and we relate them to classical Quillen metrics in a formula where the Gillet-Soulé genus R appears.

This formula is parallel to a formula we had proved with Lebeau for Ray-Singer metrics in the context of de Rham theory. We develop the theory in the equivariant setting, and also for holomorphic torsion Cited by: 8. The relevant hypoelliptic deformation of the Laplacian in the case of Riemann surfaces of constant negative curvature is briefly described, in connection with Selberg's trace formula.

The hypoelliptic Laplacian and Ray-Singer metrics, Annals of Mathematics Studies,Princeton University Press, Princeton, NJ, Cited by:.

The Hypoelliptic Laplacian and Ray-Singer Metrics Jean-Michel Bismut & Gilles Lebeau The Structure of Affine Buildings Richard M. Weiss Classifying Spaces of Degenerating Polarized Hodge Structures Kazuya Kato & Sampei Usui Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical.The secondary classes for two metrics 22 Determinant bundle and Ray-Singer metric 23 Chapter 2.

The hypoelliptic Laplacian on the cotangent bundle 25 A deformation of Hodge theory 25 The hypoelliptic Weitzenb¨ock formulas 29 Hypoelliptic Laplacian and standard Laplacian 30File Size: KB. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic : János Kollár.