arXiv subjects

P. B. Gilkey

Publications and source records attributed to P. B. Gilkey.

7 recordsLinked to original sources

arXiv2020

Harmonic radial vector fields on harmonic spaces

We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian $Δ^0$ on functions and the Laplacian $Δ^1$ on 1-forms. We examine the nature of the singularity as the geodesic distance $r$ tends to zero of radial eigen-functions and 1-forms. Via duality, our results give rise to corresponding results for radial vector fields. Many of our results extend to the context of spaces which are harmonic with respect to a single point.

math.DG↗

arXiv2018

Affine Killing complete and geodesically complete homogeneous affine surfaces

An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution space of the quasi-Einstein equation to examine these concepts in the setting of homogeneous affine surfaces.

math.DG↗

arXiv2003

Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product manifolds of arbitrary even dimension.

hep-th↗

arXiv2001

Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal anomaly in quantum brane-world scenario.

hep-th↗

arXiv2000

Heat asymptotics with spectral boundary conditions II

Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.

math-ph↗

arXiv2000

Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary

Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying Tr Qe^{-tD}, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.

hep-th↗

arXiv1999

Heat kernel asymptotics with mixed boundary conditions

We calculate the coefficient $a_5$ of the heat kernel asymptotics for an operator of Laplace type with mixed boundary conditions on a general compact manifold.

hep-th↗