17 citations · 143 across the 69 of their papers we have counts for
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Derived heat trace asymptotics for the de Rham and Dolbeault complexes
Jesús A. Álvarez López, Peter B. Gilkey
We examine the derived heat trace asymptotics in both the real and the complex settings for a generalized Witten perturbation. If the dimension is even, in the real context we show…
The Witten deformation of the Dolbeault complex
Jesús Álvarez López, Peter Gilkey
We introduce a Witten-Novikov type perturbation of the Dolbeault complex of any complex Kähler manifold, defined by a form of type with $\partial…
An almost Zoll affine surface
Peter B Gilkey
An affine surface is said to be an affine Zoll surface if all affine geodesics close smoothly. It is said to be an affine almost Zoll surface if thru any point, every affine geodes…
The local index density of the perturbed de Rham complex
Jesús Álvarez-López, Peter Gilkey
A closed 1-form on a manifold induces a perturbation of the de~Rham complex. This perturbation was originally introduced Witten for exact , and later extended by Novik…
Harmonic spaces
Peter Gilkey, JeongHyeong Park
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 harmonic space is a symmetr…