Related papers: Heat Determinant on Manifolds

The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential…

A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…

We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection…

We consider heat kernel for higher-order operators with constant coefficients in $d$-dimensio\-nal Euclidean space and its asymptotic behavior. For arbitrary operators which are invariant with respect to $O(d)$-rotations we obtain exact…

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the…

Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…

Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the…

In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…

We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators.

Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…

We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex $\mathcal C^{1,1}$ domains. The obtained estimates precisely describe the exponential behaviour of the kernels, which has been known only in a few special…

A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate…

We consider a complete non-compact Riemannian manifold satisfying the volume doubling property and a Gaussian upper bound for its heat kernel (on functions). Let -- $\rightarrow$ $\Delta$ k be the Hodge-de Rham Laplacian on differential…

We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Caffarelli-Silvestre. While this definition in the compact case is straightforward, in the noncompact setting one…

In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also…

In this paper we investigate estimates about the Laplace operator in heat flows of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain…

We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of…