Search Results - "Gilkey, P. B."

Centrally harmonic spaces by Gilkey, P. B., Park, J. H.

“…We construct examples of centrally harmonic spaces by generalizing work of Copson and Ruse. We show that these examples are generically not centrally harmonic…”
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Heat Flow from Polygons by van den Berg, M., Gilkey, P. B., Gittins, K.

“…We study the heat flow from an open, bounded set D in ℝ 2 with a polygonal boundary ∂ D . The initial condition is the indicator function of D . A Dirichlet 0…”
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Harmonic radial vector fields on harmonic spaces by Gilkey, P.B., Park, J.H.

“…We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian Δ0 on functions and the Laplacian Δ1 on…”
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Generalized osserman manifolds by Gilkey, P. B.

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Harmonic Spaces and Density Functions by Gilkey, P. B., Park, J. H.

“…We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the…”
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HEAT CONTENT AND A HARDY INEQUALITY FOR COMPLETE RIEMANNIAN MANIFOLDS by VAN DEN BERG, M., GILKEY, P. B.

“…Upper bounds are obtained for the heat content and the torsional rigidity of a complete Riemannian manifold $M$, assuming a Hardy inequality for the Dirichlet…”
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HEAT CONTENT ASYMPTOTICS WITH TRANSMITTAL AND TRANSMISSION BOUNDARY CONDITIONS by GILKEY, P. B., KIRSTEN, K.

“…The heat content asymptotics on a Riemannian manifold with smoooth boundary defined by Dirichlet, Neumann, transmittal and transmission boundary conditions are…”
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Symmetric affine surfaces with torsion by D’Ascanio, D., Gilkey, P.B., Pisani, P.

“…We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion…”
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The Witten deformation of the Dolbeault complex by Álvarez López, J., Gilkey, P.

“…We introduce a Witten–Novikov type perturbation ∂ ¯ ω ¯ of the Dolbeault complex of any complex Kähler manifold, defined by a form ω of type (1, 0) with ∂ ω =…”
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A COMPARISON ESTIMATE FOR THE HEAT EQUATION WITH AN APPLICATION TO THE HEAT CONTENT OF THE S-ADIC VON KOCH SNOWFLAKE by VAN DEN BERG, M., GILKEY, P. B.

“…Let D be an open set in Euclidean space IRm with boundary ∂D, and let ϕ[ratio ]∂D→[0, ∞) be a bounded, measurable function. Let u[ratio ]D∪∂D×[0, ∞)→[0, ∞) be…”
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The eta invariant and theK-theory of odd dimensional spherical space forms by Gilkey, P. B.

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The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics by Gilkey, P. B., Park, J. H.

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Harmonic radial vector fields on harmonic spaces by Gilkey, P. B, Park, J. H

“…We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian $\Delta^0$ on functions and the Laplacian…”
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Affine Killing complete and geodesically complete homogeneous affine surfaces by Gilkey, P. B, Park, J. H, Valle-Regueiro, X

“…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…”
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Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario by Gilkey, Peter B., Kirsten, Klaus, Vassilevich, Dmitri V.

“…We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate the first several coefficients of the heat…”
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Heat kernel asymptotics with mixed boundary conditions by Branson, Thomas P., Gilkey, Peter B., Kirsten, Klaus, Vassilevich, Dmitri V.

“…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…”
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Szabo Osserman IP pseudo-Riemannian manifolds by Gilkey, Peter B., Ivanova, Raina, Zhang, Tan

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Leading Terms in the Heat Invariants by Branson, Thomas P., Gilkey, Peter B., Ørsted, Bent

“…Let D be a second-order differential operator with leading symbol given by the metric tensor on a compact Riemannian manifold. The asymptotics of the heat…”
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Heat asymptotics with spectral boundary conditions II by Gilkey, P. B, Kirsten, K

“…Proc.Roy.Soc.Edinburgh A133 (2003) 333-361 Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral…”
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Logarithmic terms in asymptotic expansions of heat operator traces by Gilkey, Peter B., Grubb, Gerd

“…Let P be an elliptic selfadjoint positive classical pseudodifferential operator of order d on a compact m-dimensional manifold without boundary. The heat trace…”
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