相关论文: Spectral Geometry of Riemannian Submanifolds

This paper is devoted to investigate the heat trace asymptotic expansion corresponding to the magnetic Steklov eigenvalue problem on Riemannian manifolds with boundary. We establish an effective procedure, by which we can calculate all the…

Let $\mathcal{M}$ be a smooth, closed and connected manifold of dimension $n\in\mathbb{N}$, endowed with a Riemannian metric $g$. Moreover, let $\mathcal{B}$ be an $(n+1)$-dimensional compact manifold with boundary equal to $\mathcal{M}$.…

We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…

We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace of this operator has a particular short time asymptotic expansion. The coefficients in this expansion…

For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the…

This paper is devoted to study the asymptotic expansion of the heat trace of the Dirichlet-to-Neumann map for the thermoelastic equation on a Riemannian manifold with doundary. By providing a method we can obtain all the coefficients of the…

Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.

We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley [BS]. In the…

We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our…

Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.

The existence of a full asymptotic expansion for the heat content asymptotics of an operator of Laplace type with classical Zaremba boundary conditions on a smooth manifold is established. The first three coefficients in this asymptotic…

Let $(M,g)$ be a surface with Riemannian metric and curved conic singularities. More precisely, a neighbourhood of a singularity is isometric to $(0,1)\times S^1$ with metric $g_{\text{conic}}=dr^2+f(r)^2d\theta^2, r\in(0,1)$. We study the…

Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish the…

We study the spectral properties of the scalar Laplacian on a $n$-dimen\-sional warped product manifold $M=\Sigma\times_f N$ with a $(n-1)$-dimensional compact manifold $N$ without boundary, a one dimensional manifold $\Sigma$ without…

In this work we study the asymptotics of the fractional Laplacian as $s\to 0^+$ on any complete Riemannian manifold $(M,g)$, both of finite and infinite volume. Surprisingly enough, when $M$ is not stochastically complete this asymptotics…

Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this…

Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we…

We establish a global rigidity theorem for Riemannian metrics without conjugate points on three-manifolds of the form $M = \Sigma \times S^1$, where $\Sigma$ is a compact orientable surface of genus at least 2. The main result states that…

We study the heat trace for both the drifting Laplacian as well as Schr\"odinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term)…

We obtain the asymptotic expansions of the traces of the thermoelastic operators with the Dirichlet and Neumann boundary conditions on a Riemannian manifold, and give an effective method to calculate all the coefficients of the asymptotic…