arXiv research

Study shows convergence rates for Cheeger cuts on data clouds.

The paper proves inequalities for Steklov eigenvalues on finite graphs.

The paper studies eigenvalue problems on manifolds and recovers known inequalities.

Solved Cheeger inequalities for simplicial complexes, combining topological and graph theoretic methods.

Investigates Cheeger sets in rotationally invariant domains and their free boundaries.

We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian $n$-manifolds. For some non-compact, finite area 2-manifolds, we prove the existence and regularity of subsets whose isoperimetric ratio is equal to the Cheeger constant. To do this, we us…

We prove Cheeger-Gromov convergence for a subsequence of a given sequence of manifolds-with-boundary of bounded geometry. The method of the proof is to reduce, via height functions, the problem to the setting of Hamilton's compactnes theorem for manifolds without boundary.

New upper bound for Cheeger constant of hyperbolic surfaces.

Simplified proof for Cheeger's isoperimetric constant.

Solves linearity problem for acyclic groups, bounds Cheeger-Gromov ρ-invariants.

Extends Cheeger's method to Lie groupoid actions on manifolds.

Sharp stability results for reverse isoperimetric inequalities in 2D.

The Cheeger constant increases under Ricci flow on spheres.

We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons …

In [Cheeger-Tian 2005], Cheeger-Tian proved an $ε$-regularity theorem for $4$-dimensional Einstein manifolds without volume assumption. They conjectured that similar results should hold for critical metrics with constant scalar curvature, shrinking Ricci solitons, Ricci flows in $4$-dimensional manifolds and higher dim…

We introduce notions of Cheeger constants for graphons and graphings. We prove Cheeger and Buser inequalities for these. On the way we prove co-area formulae for graphons and graphings.

Study on Cheeger constant in specific hyperbolic 3-manifolds.

New inequality for special forms on manifolds.

Lower bounds for eigenvalues on manifolds with boundary conditions.

We prove the Novikov conjecture on oriented Cheeger spaces whose fundamental group satisfies the strong Novikov conjecture. A Cheeger space is a stratified pseudomanifold admitting, through a choice of ideal boundary conditions, an L2-de Rham cohomology theory satisfying Poincare duality. We prove that this cohomology …

Study calculates Cheeger constants and small eigenvalues of Maass cusp forms.

Random hyperbolic surfaces have low Cheeger constants.

The paper bounds Cheeger ratios of eigenfunctions and their level sets.

In this paper, we consider Cheeger's constant and the first eigenvalue of the nonlinear Laplacian on closed Finsler manifolds. Being based on these, we establish Cheeger's inequality and Buser's inequality for closed Finsler manifolds.

Generalizes Cheeger inequality to Carnot-Carathéodory spaces.

Study Cheeger inequalities for Riemannian manifolds with boundary.

We show that Cheeger deformations regularize $G$--invariant metrics in a very strong sense.

The Cheeger-Gromoll theorem is adapted for groups, revealing geometric properties of virtually abelian groups.

Negative curvature manifolds have vanishing bounded volume class if and only if Cheeger constant is positive.

Paper extends variational formula for Bismut-Cheeger eta form, proving key theorems in K-theory.

There are two natural candidates for the group of relative Cheeger-Simons differential characters. The first directly extends the work of Cheeger and Simons and the second extends the description given by Hopkins and Singer of the Cheeger-Simons group as the homology of a certain cochain complex. We discuss both approa…

We prove a Cheeger inequality for the first positive Steklov eigenvalue. It involves two isoperimetric constants.

We prove a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Ste…

In this paper, we mainly establish a Cheeger type finiteness theorem for Berwald manifolds. In order to do this, we study the injectivity radius and the convex radius of a Finsler manifold. A Cheeger type estimate on injectivity radii for Finsler manifolds is given and the existence of the center of mass of a Berwald m…

In this paper we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. Furthermore, we…

Let $(X,d,μ)$ be a complete metric measure space, with $μ$ a locally doubling measure, that supports a local weak $L^2$-Poincaré inequality. By assuming a heat semigroup type curvature condition, we prove that Cheeger-harmonic functions are Lipschitz continuous on $(X,d,μ)$. Gradient estimates for Cheeger-harmonic func…

The paper improves estimates on singular sets in manifolds with integral curvature bounds.

This is a short survey of Cheeger and Kleiner's nonembeddability theorem for Heisenberg group into $L^1$.

We investigate conformality of the differential of a mapping between Riemannian manifolds if the tangent bundles are equipped with a generalized metric of Cheeger-Gromoll type.

In this paper, we study eigenvalues and eigenfunctions of $p$-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of $p$-Laplacian, as $p\to 1,$ we ident…

New proofs of Cheeger-like inequalities for coexact 1-forms on hyperbolic manifolds.

In this paper, we prove two generalized versions of the Cheeger-Gromoll splitting theorem via the non-negativity of the Bakry-Émery Ricci curavture on complete Riemannian manifolds.

We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group $G$ with Lie algebra $\G$ is $h(G)=\max_{H\in\G,||H||=1} \tr(\ad (H))$.

Paper connects probability density cuts to graph theory eigenfunctions.

New metric measure space theory for Lipschitz constants.

In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Bruening-Ma's Cheeger-Mueller type theorem…

The study extends a theorem to bundles on manifolds with boundaries.

We obtain an estimate of the Cheeger isoperimetric constant in terms of the volume growth for a properly immersed submanifold in a Riemannian manifold which possesses at least one pole and sectional curvature bounded from above .