Related papers: Heat kernels, symplectic geometry, moduli spaces a…
The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to…
We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
Special case calculations are presented, which can be used to put restrictions on the general form of heat kernel coefficients for transmittal boundary conditions and for generalized bag boundary conditions.
Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…
The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related…
We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping…
The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact,…
In this paper, we study a subelliptic heat kernel on the Lie group SL(2,R) and on its universal covering. The subelliptic structure on SL(2,R) comes from the fibration $SO(2) -> SL(2,R) -> H^2$ and it can be lifted to its universal…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $\Omega=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra…
In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of…
By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…