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When the leading terms in the heat equation asymptotics are coercive. (English) Zbl 0836.58040

Authors’ abstract: “Let \(M\) be a compact Riemannian manifold without boundary of dimension \(m\geq 2\). Let \(a_n(D)\) be the asymptotics of the heat equation for \(n\geq 3\). If \(D\) is the \(p\)-form valued Laplacian for \(0\leq p\leq m\), the \(a_n\) lead to coercive estimates for the highest order jets of the covariant derivatives of the curvature tensor for any \(n\). If \(D\) is the conformal Laplacian, the \(a_n\) lead to coercive estimates if and only if \(2n\not\in \{m- 2, m- 1, m\}\). If \(D\) is the spinor Laplacian, the \(a_n\) lead to coercive estimates if and only if \(2n> m\)”.

MSC:

58J37 Perturbations of PDEs on manifolds; asymptotics
58J35 Heat and other parabolic equation methods for PDEs on manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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