arXiv research

Established a Hardy inequality on Finsler manifolds.

Kähler information manifolds for signal filters in weighted Hardy spaces are explored.

Simple proof of Hardy inequality on Carnot groups and hypoelliptic vector fields.

Study Hardy identities and inequalities on Cartan-Hadamard manifolds.

New potential theory on minimal hypersurfaces shows stable growth of solutions near singularities.

The paper proves new Hardy inequalities on closed manifolds using Ricci curvature.

Study finds loops with specific curvature exist using Hardy's inequality.

The study calculates best Sobolev constants with sharp Hardy terms in Euclidean and hyperbolic spaces.

Sharp Hardy inequalities on Riemannian submanifolds with non-negative curvature.

The paper proves Hardy inequalities on Finsler manifolds using superharmonicity.

Paper finds best constants in Hardy inequalities on Finsler metric measure manifolds.

Sharp Hardy and spectral gap inequalities found on special irreversible Finsler manifolds.

Study on pseudo-Einstein 3-manifolds for a specific inequality, introducing Robin mass.

This paper establishes inequalities on quaternionic hyperbolic spaces and the Cayley hyperbolic plane.

Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved by Michael-Simon and Hoffman-Spruck. Since then, a sort of applications to the submanifold theory has been derived from those inequalities. …

Extends Riemannian geometry inequalities with sharper estimates.

Proves inequalities on curved spaces with positive curvature.

New concept of regular separation for ODEs leads to improved Hardy field results.

The paper derives inequalities on Finsler manifolds, influenced by their curvatures.

Sharp inequalities on Siegel domains and complex hyperbolic spaces established.

The paper proves the existence of infinite sign-changing solutions to a Hardy-Sobolev equation on Riemannian manifolds.

Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $L^q$ regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of $\mathbb{R}^n$, which imply asymptotic behavior of the solutions at i…

We obtain upper bounds on the heat content and on the torsional rigidity of a complete Riemannian manifold M, assuming a generalized Hardy inequality for the Dirichlet Laplacian on M.

In this article, we obtain a strict inequality between the conjugate Hardy $H^{2}$ kernels and the Bergman kernels on planar regular regions with $n>1$ boundary components, which is a conjecture of Saitoh.

Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.

Given a compact Riemannian Manifold (M,g) of dimension n > 2, a point x_0 in M and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. The Hardy-Sobolev embedding yields the existence of A,B > 0 such that (\int_M|u|^{2*(s)}dv_g)^{2/2*(s)} \leq A\int_M |\nabla u|_g^2 dv_g +B\int_M u^2 dv_g fo…

The paper examines eigenvalues and inequalities on Riemannian manifolds.

The paper confirms a conjecture about Hardy-Sobolev-Maz'ya inequalities and Green's functions on hyperbolic spaces.

We investigate the possibility of improving the $p$-Poincaré inequality $\|\nabla_{\mathbb{H}^N} u\|_p \ge Λ_p \|u\|_p$ on the hyperbolic space, where $p>2$ and $Λ_p:=[(N-1)/p]^{p}$ is the best constant for which such inequality holds. We prove several different, and independent, improved inequalities, one of which is …

We prove certain generalization of Hardy's inequality where the "boundary defining function" is replaced by a polynomial defining a singular algebraic variety. An application is given on the existence of a small time heat trace expansion for a Schrödinger operator with mild singularities along this algebraic set.

We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptoticall…

Local Hardy spaces defined for Riemannian manifolds with bounded geometry.

Alternative proofs for various inequalities on Riemannian manifolds.

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincaré inequality, the space $\Mone$, defined by Hajłasz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homoge…

In this paper, we study the sharp constants of quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds equipped with arbitrary measures. In particular, these inequalities can be globally refined by adding remainder terms like the Brezis-Vázquez improvement, if Finsler manifolds are of strictly ne…

Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the $H^p$-boundedness for Riesz transforms on $M$, g…

Study on Hardy-Littlewood maximal operators on manifolds with bounded geometry.

In this paper, we show the equivalence between the boundedness of the Riesz transform $dΔ^{-1/2}$ on $L^p$, $p\in (2,p_0)$, and the equality $H^p=L^p$, $p\in(2,p_0)$, in the class of manifold whose measure is doubling and for which the scaled Poincaré inequalities hold. Here, $H^p$ is a Hardy space of exact $1-$forms, …

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most exponential volume growth. In particular, if $D$ is the Hodge--Dirac operator on $…

The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.

Study spectral properties on manifolds with conical singularities, proving new inequalities.

Let (M,g) be a compact Riemannien Manifold of dimension n > 2, x_0 in M a fix and singular point and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. we investigate the existence of positive distributional solutions u in C^0(M) to the critical equation Δ_g u + a(x) u = u^{2*(s)-1}/ d_g(x,…

The study improves Poincaré and log-Sobolev inequalities on hyperbolic spaces.

Paper uses Gromov-Hausdorff convergence to re-examine surface classification.

The study establishes bounds for Schrödinger operators on Riemannian manifolds.

The paper explores how Finsler manifolds differ from Riemannian ones in functional inequalities.

New methods for multivariate nonparametric regression reduce dimensionality issues.

The paper bounds Fourier integral operators on Hardy spaces with specific conditions.