arXiv research

Paper introduces magnetic Hodge Laplacian for differential forms.

BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.

Study shows equality in Hodge Laplacian bound occurs only on spheres.

Lower bounds for Hodge-Laplacian spectrum on orbifolds.

Study Hodge Laplacians for manifold data, improving error bounds.

A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.

We study multiplicity of the eigenvalues of the Hodge Laplacian on smooth, compact Riemannian manifolds of dimension five for generic families of metrics. We prove that generically the Hodge Laplacian, restricted to the subspace of co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is based on t…

In this paper, we obtain "universal" inequalities for eigenvalues of the weighted Hodge Laplacian on a compact self-shrinker of Euclidean space. These inequalities generalize the Yang-type and Levitin-Parnovski inequalities for eigenvalues of the Laplacian and Laplacian. From the recursion formula of Cheng and Yang \ci…

Novel Hodge theory developed for Carrollian bundles, addressing black hole event horizons.

Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.

Constructs metrics with zero eigenvalues for Hodge-Laplacian.

Rough and Hodge Laplacians eigenvalues approach zero with fixed volume.

We consider a family of compact, oriented and connected Riemannian manifolds shrinking to a metric graph and describe the asymptotic behaviour of the eigenvalues of the Hodge Laplacian. We apply our results to produce manifolds with spectral gaps of arbitrarily large size in the spectrum of the Hodge Laplacian.

In this paper, we derive a gradient estimate for the linear combinations of eigenforms of the Hodge Laplacian on a closed manifold. The estimate is given in terms of the dimension, volume, diameter and curvature bound of the manifold. As an application, we obtain directly a sharp estimate for the heat kernel of the Hod…

The paper proves estimates for Hodge Laplacians on Lie groups.

Proves spectral simplicity of Hodge Laplacian and curl operator along metric families.

An adapted version of the proof (due to A. Weil) of the well-known de Rham Theorem allows us to compare uniformly the spectrum of the Hodge Laplacian acting on differential forms (on a compact Riemannian manifold) to the spectrum of the combinatorial Laplacian acting on cochains associated to an open cover (made of bal…

Introduces a new Hodge theory using vector fields on manifolds.

Eigenvalue estimates for Hodge Laplacian on Fano manifolds lead to geometric insights.

Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.

In the present paper, we consider the Hodge-de Rham Laplacian that acts on conformal Killing and projective Killing one-forms of a compact Riemannian manifold.

Uniform eigenvalue bounds for Hodge Laplacian on manifolds with Ricci curvature and injectivity radius bounds.

Study shows eigenvalue of Hodge Laplacian on coexact 1-forms in hyperbolic 3-manifolds is related to isoperimetric ratio.

Eigenvalue estimates for weighted manifolds with applications.

Proves tropical Hodge theory for smooth projective varieties, conditional on Laplacian regularity.

Study on Hodge theory for almost complex manifolds.

Study on $G_2$-structures using Laplacian coflow and solitons.

Method detects trajectory outliers using Hodge Laplacian embeddings.

We give some sharp lower bounds of the first eigenvalue for the Hodge Laplacian acting on differential forms on the boundary of a Riemannian manifold. We also give some sharp estimates for the first nonzero Steklov eigenvalue for differential forms.

The paper develops a new Laplacian for manifold learning from data.

Researchers compute the spectrum of Hodge-Laplacian on 1-forms for SU(2) and SO(3).

New method generalizes eigenvalue inequality to surfaces with boundaries.

Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds

The Hodge spectra help distinguish orbifolds from manifolds with singularities.

The paper studies Hodge Laplacians from point clouds, proving spectral convergence and harmonic form consistency.

The paper extends Hodge-de Rham and Lichnérowicz Laplacians to double forms and proves vanishing theorems.

We prove $R$-bisectoriality and boundedness of the $H^\infty$-functional calculus in $L^p$ for all $1<p<\infty$ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery Ricci curvature on $k$-forms.

Let $g$ and $\tilde{g}$ be Riemannian metrics on a noncompact manifold $M$, which are conformally equivalent. We show that under a very mild \emph{first order} control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians $Δ_g$ and $Δ_{\tilde{g}}$ acting on differential forms exist and are c…

On any compact manifold of dimension greater than 3, we exhibit a metric whose first positive eigenvalue for the Laplacian acting on p-form is of multiplicity 2. As a corollary, we prescribe the volume and any finite part of the spectrum of the Hodge Laplacian with multiplicity 1 or 2.

New method for manifold topological learning avoids remeshing issues.

We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. T…

What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidate different aspects of different Laplace operators such as de Rham-Hodge Laplacian as well as Ebin-Marsden's Laplacian. A probabilistic repr…

Derives integral formula for differential forms on compact spaces with applications.

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stron…

Study Morse-Novikov cohomology on foliated manifolds and prove Hodge theorem.

We present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian

Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operator and the Hodge-Kodaira Laplacian acting on functions has discrete spectrum. Moreover we provide some estimates for the growth of the corre…

Paper introduces signal processing on cell complexes.