scholarly journals Riemannian flows and adiabatic limits

2018 ◽  
Vol 29 (02) ◽  
pp. 1850011
Author(s):  
Georges Habib ◽  
Ken Richardson
Keyword(s):  
Dirac Operator ◽  
Spin Manifold ◽  
Convergence Properties ◽  
Adiabatic Limits ◽  
Riemannian Flows ◽  
Riemannian Flow

We show the convergence properties of the eigenvalues of the Dirac operator on a spin manifold with a Riemannian flow when the metric is collapsed along the flow.

scholarly journals Boundary Value Problems for the Lorentzian Dirac Operator

2018 ◽  
pp. 3-18
Author(s):  
Christian Bär ◽  
Sebastian Hannes
Keyword(s):  
Riemannian Manifold ◽  
Dirac Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Classical Case ◽  
Spin Manifold ◽  
Globally Hyperbolic ◽  
Manifold With Boundary ◽  
Smooth Space

On a compact globally hyperbolic Lorentzian spin manifold with smooth space-like Cauchy boundary, the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah–Patodi–Singer boundary conditions are imposed. This chapter explores to what extent these boundary conditions can be replaced by more general ones and how the index then changes. There are some differences to the classical case of the elliptic Dirac operator on a Riemannian manifold with boundary.

scholarly journals Twistor spaces and the adiabatic limits of Dirac operators

2001 ◽  
Vol 164 ◽  
pp. 53-73 ◽  
Author(s):  
Masayoshi Nagase
Keyword(s):  
Dirac Operator ◽  
Spin Structure ◽  
Twistor Space ◽  
Dirac Operators ◽  
Twistor Spaces ◽  
Adiabatic Limits ◽  
Twisted Dirac Operator

We show that a (Spinq-style) twistor space admits a canonical Spin structure. The adiabatic limits of η-invariants of the associated Dirac operator and of an intrinsically twisted Dirac operator are then investigated.

scholarly journals A Weighted L2-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds

2007 ◽  
Vol 59 (5) ◽  
pp. 943-965 ◽  
Author(s):  
Felix Finster ◽  
Margarita Kraus
Keyword(s):  
Dirac Operator ◽  
Scalar Curvature ◽  
Spin Manifold ◽  
Lowest Eigenvalue ◽  
L2 Estimate

AbstractWe derive a weighted L2-estimate of theWitten spinor in a complete Riemannian spin manifold (Mn, g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of M.

Existence Results for Solutions to Nonlinear Dirac Systems on Compact Spin Manifolds

2018 ◽  
Vol 18 (1) ◽  
pp. 87-104
Author(s):  
Xu Yang
Keyword(s):  
Dirac Operator ◽  
Growth Rates ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Spin Manifold ◽  
Dirac System ◽  
Nontrivial Solutions ◽  
Subcritical Growth ◽  
Dirac Systems ◽  
Spin Manifolds

AbstractIn this article, we study the existence of solutions for the Dirac system\left\{\begin{aligned} \displaystyle Du&\displaystyle=\frac{\partial H}{% \partial v}(x,u,v)\quad\text{on }M,\\ \displaystyle Dv&\displaystyle=\frac{\partial H}{\partial u}(x,u,v)\quad\text{% on }M,\end{aligned}\right.whereMis anm-dimensional compact Riemannian spin manifold,{u,v\in C^{\infty}(M,\Sigma M)}are spinors,Dis the Dirac operator onM, and the fiber preserving map{H:\Sigma M\oplus\Sigma M\rightarrow\mathbb{R}}is a real-valued superquadratic function of class{C^{1}}with subcritical growth rates. Two existence results of nontrivial solutions are obtained via Galerkin-type approximations and linking arguments.

Dirac operators on the S3 and S2 spheres

2017 ◽  
Vol 14 (08) ◽  
pp. 1740005 ◽  
Author(s):  
Fabio di Cosmo ◽  
Alessandro Zampini
Keyword(s):  
Dirac Operator ◽  
Spectral Resolution ◽  
Dirac Operators ◽  
Spin Manifold ◽  
De Rham

We describe both the Hodge–de Rham and the spin manifold Dirac operator on the spheres [Formula: see text] and [Formula: see text], following the formalism introduced by Kähler, and exhibit a complete spectral resolution for them in terms of suitably globally defined eigenspinors.

Convergence properties of hit-and-run samplers

1998 ◽  
Vol 14 (4) ◽  
pp. 767-800
Author(s):  
Claude Bélisle ◽  
Arnon Boneh ◽  
Richard J. Caron
Keyword(s):  
Convergence Properties ◽  
Hit And Run
Sign in / Sign up

Export Citation Format

Share Document