Estimates for the classical parametrix for the Laplacian |
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Authors: | Steven Zucker |
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Institution: | (1) Department of Mathematics, Rutgers College, 08903 New Brunswick, New Jersey, USA |
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Abstract: | We consider the integral operators which were used classically to give a parametrix and remainder for the Laplacian on a Riemannian manifold. Their kernels are defined in terms of the distance function. These operators are shown to be bounded operators on the L2 Hilbert spaces of differential forms, under the hypotheses that the manifold be complete and of finite volume, and that it satisfy curvature bounds. Furthermore, the remainder is shown to be compact. |
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