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- W1646042973 abstract "In this thesis we study the geometry of the fixed point set $Sigma$ of a smooth mapping $Phi: Mto M$ on a smooth compact Riemannian manifold $M$ without boundary by computing the asymptotic expansion of the deformed heat trace $Trace Phiexp(tDelta)$ of the Laplace operator $Delta$ on $M$. We assume that the fixed point set $Sigma$ is a union of connected components, each of which is a smooth compact submanifold of $M$ without boundary. The deformed heat trace asymptotics is determined by contributions of each connected component, so each of them can be studied separately. We develop a generalized Laplace method for computing the coefficients of this asymptotic expansion and compute the first three coefficients explicitly in the following cases: 1) zero- and one-dimensional components of the fixed point set of $Phi$ in a flat two-dimensional manifold; 2) zero-dimensional component of the fixed point set of $Phi$ in a curved manifold." @default.
- W1646042973 created "2016-06-24" @default.
- W1646042973 creator A5040194210 @default.
- W1646042973 date "2005-07-21" @default.
- W1646042973 modified "2023-09-27" @default.
- W1646042973 title "Spectral Geometry of Riemannian Submanifolds" @default.
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