arXiv research

We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansion…

We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace type operators.

The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we first provide a decomposition of the higher spin Laplace operator in terms of Rr…

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All of the Laplace opera…

Let $P$ be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various $P$-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…

We study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We consider I and III Laplace-Beltrami operator surfaces of a TF-type surface. Then we obtain degrees and classes of algebraic surfaces of the surfaces using eliminate methods on software…

The purpose of this note is to provide a short cut presentation of a Mayer-Vietoris formula due to Burghelea-Friedlander-Kappeler for the regularized determinant in the case of elliptic operators of Laplace Beltrami type in the form typically needed in applications to torsion.

Upper bounds for Steklov eigenvalues on curved submanifolds.

We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results obtained earlier for the scalar Laplacian and present closed formulas for all heat in…

Solves geodesics and Laplace-Beltrami spectrum on flag manifolds.

Study $f$-Laplace bounds on gradient Ricci shrinkers, applying to Betti numbers.

Symmetry proven for positive solutions of a weighted p-Laplace operator inequality.

Study spectral functionals on manifolds with torsion.

Bounds on spectral gaps of hyperbolic 3-manifolds and orbifolds.

This paper computes a heat coefficient for nonminimal Laplace type operators.

It is shown that the estimates obtained by Manfredo P. do Carmo and Detang Zhou, in their paper "Eigenvalue estimate on complete noncompact Riemannian manifolds and applications", for the first eigenvalue of the Laplace-Beltrami operator on open manifolds, via an oscillation theorem, can be naturally extended for the s…

In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…

Study on 2-ruled hypersurfaces in a Walker 4-manifold.

We study the third Laplace-Beltrami operator of timelike rotational surface of (T,L)-type in three dimensional Lorentz-Minkowski space.

The paper proves Schauder estimates for Laplace-Beltrami on manifolds with fibered boundaries.

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^μ\N_μ$. Our objective is to obtain information on the asymptotic expansions of the corresponding r…

Introduces a new elliptic operator with positive eigenvalue.

Study new spectral invariants for Laplace and Dirac operators on manifolds.

Study properties of surfaces with nonvanishing third fundamental form.

Study essential spectrum of differential operators on geometrically finite orbifolds.

New solutions found for Ginzburg-Landau equations on complex manifolds.

Let $Ł$ be the Laplace operator on $\R ^d$, $d\geq 3$ or the Laplace Beltrami operator on the harmonic $NA$ group (in particular on a rank one noncompact symmetric space). For the equation $Łu - \varphi(\cdot,u)=0$ we give necessary and sufficient conditions for the existence of entire bounded or large solutions under…

The paper constructs Laplace-Beltrami operators on noncommutative tori.

Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.

We obtain an off-diagonal upper bound for Green and heat kernel of Laplace type operator on symmetric spaces.

In this paper, we would like to give an answer to \textbf{Problem 1} below issued firstly in [J. Mao, Eigenvalue estimation and some results on finite topological type, Ph.D. thesis, IST-UTL, 2013]. In fact, by imposing some conditions on the mean curvature of the initial hypersurface and the coefficient function of th…

The paper studies graph Laplace operator behavior near isolated singularities.

The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…

Study of spectral geometry on noncommutative tori using functional metrics.

Graph Laplace operators uniquely identify metrics and densities on manifolds.

Formula derived for Laplace-Beltrami on Stiefel manifold.

We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …

Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.

We present a generalization of the Clifford action for other representations spaces of $Spin(n)$, which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In particular, we have general Bochner identities for them, and an eigenvalue estimate o…

Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

We study Bakry-Emery type estimates for the Laplace-Beltrami operator of a totally geodesic foliation. In particular, we are interested in situations for which the $Γ_2$ operator may not be bounded from below but the horizontal Bakry-Emery curvature is. As we prove it, under a bracket generating condition, this weaker …

In this paper, we mainly investigate continuity, monotonicity and differentiability for the first eigenvalue of the $p$-Laplace operator along the Ricci flow on closed manifolds. We show that the first $p$-eigenvalue is strictly increasing and differentiable almost everywhere along the Ricci flow under some curvature a…

This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.

Method finds domain of Laplace-Beltrami operator on 2D almost-Riemannian manifolds.

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eige…

Stochastic representation for determinants derived from Brownian loop soups.

The study establishes inequalities for functions on manifolds using Green function estimates.