arXiv research

Direct proof of Neumann isoperimetric inequality for convex domains.

Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.

Sharp inequality outside ball proved using Neumann method.

Paper derives inequalities for eigenvalues of Witten-Laplacian under fixed volume constraint.

Geodesic disks maximize the first non-trivial Neumann eigenvalue on spheres.

Study on Neumann eigenvalues controlled by domain isoperimetric ratio.

} In this article, we put forward a Neumann eigenvalue problem for the bi-harmonic operator $Δ^2$ on a bounded smooth domain $\Om$ in the Euclidean $n$-space ${\bf R}^n$ ($n\ge2$) and then prove that the corresponding first non-zero eigenvalue $Υ_1(\Om)$ admits the isoperimetric inequality of Szegö-Weinberger type: $Υ_…

Proven isoperimetric inequality for Witten-Laplacian eigenvalues.

We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of $\mathbb{R}^n$. Our result applies to…

We prove that the isoperimetric profile of a convex domain $Ω$ with compact closure in a Riemannian manifold $(M^{n+1},g)$ satisfies a second order differential inequality which only depends on the dimension of the manifold and on a lower bound on the Ricci curvature of $Ω$. Regularity properties of the profile and top…

Let $M$ be a compact Riemannian manifold with boundary $\pp M$ and $L= \DD+Z$ for a $C^1$-vector field $Z$ on $M$. Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by $L$, are presented for lower bound conditions on the curvature of $L$ …

Study fine Pólya-Szegő inequalities in metric spaces with applications.

Researchers derive asymptotic expansions for thermoelastic operators on manifolds.

Paper bounds the A-hat genus using curvature and isoperimetric constants.

The isoperimetric inequality and related inequalities are explored.

The paper finds new inequalities for convex polygons.

Study on Riemannian isoperimetric inequality, finding it true generically.

The paper proves new inequalities in hyperbolic space using Euclidean methods.

New proof of isoperimetric inequality using Steiner's formula.

Study improves isoperimetric inequality for random groups.

The study proves analogues of the discrete isoperimetric inequality in hyperbolic geometry.

Proves optimal isoperimetric inequality in de Sitter space.

Sharp isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature.

Proves an isoperimetric inequality for diffused surfaces.

The paper characterizes hyperbolic manifolds and graphs verifying a specific isoperimetric inequality.

The study finds a special isoperimetric inequality for minimal hypersurfaces in spheres.

Solves equality case in isoperimetric inequality for non-convex domains.

Prove an isoperimetric inequality for compact bodies in 3D contact non-unimodular Lie groups.

Sharp isoperimetric inequality for minimal submanifolds in 2D and higher Euclidean space.

Proves a reverse isoperimetric inequality in curved spaces.

New findings on metric spaces with finite Nagata dimension.

Study eigenvalues and shapes, proving sharp inequalities for Steklov eigenvalues.

New inequalities for planar convex domains' Laplacian eigenvalues.

Quantifies fractional isoperimetric inequality with strong control over boundary oscillation.

Proof of reverse isoperimetric inequality for black holes.

The study finds inequalities in warped product manifolds linking isoperimetric and curvature integrals.

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal submanifolds of $N\times\mathbb{R}$. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fund…

Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.

Sharp curvature inequality extends Euclidean isoperimetric inequality to Cartan-Hadamard manifolds.

Researchers prove isoperimetric inequality in specific steady Ricci solitons.

New isoperimetric inequalities in the plane with radial weights identified.

Sharp bounds for curve isoperimetric deficit derived.

The study extends isoperimetric inequalities to non-positive curvature spaces.

The study connects hyperbolicity and isoperimetric inequality in manifolds and graphs.

Universal inequalities for Laplacian eigenvalues on convex domains.

Proves isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces.

Proves inequality for maximal spacelike submanifolds in Minkowski space.