Poincaŕe-Einstein holography for forms via conformal geometry in the bulk / A. Rod Gover, Emanuele Latini, Andrew Waldron.

Format:

Book

Author/Creator:

Gover, A. Rod, 1961- author.

Latini, Emanuele, 1978- author.

Waldron, Andrew (Andrew Kenneth), 1970- author.

Series:

Memoirs of the American Mathematical Society ; Volume 235, Number 1106 (first of 5 numbers)

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 235, Number 1106 (first of 5 numbers)

Language:

English

Subjects (All):

Geometry, Differential.

Particles (Nuclear physics).

Boundary value problems.

Mathematical physics--Asymptotic theory.

Mathematical physics.

Physical Description:

1 online resource (85 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

Contents:

""Cover""; ""Title page""; ""Chapter 1. Introduction""; ""Chapter 2. Bulk conformal geometry and extension problems""; ""2.1. Riemannian conventions""; ""2.2. Conformal and almost Riemannian geometry""; ""2.3. Extension problems""; ""2.4. The generalised divergence extension problem""; ""2.5. Conformal tractor calculus""; ""2.6. The calculus of scale""; ""2.7. The Laplace�Robin solution generating algebra""; ""2.8. Product solutions""; ""Chapter 3. Tractor exterior calculus""; ""3.1. Algebra of invariant operators""; ""3.2. Algebra of differential splitting operators""

""6.2. True forms""""6.3. Fundamental holographic identities""; ""Appendix A. The ambient manifold""; ""Appendix B. List of common symbols""; ""Bibliography""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-2224-7