arXiv research

The study improves Poincaré inequalities on hyperbolic space.

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

Study Hardy identities and inequalities on Cartan-Hadamard manifolds.

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

The paper proves Hardy inequalities on Finsler manifolds using superharmonicity.

Sharp inequalities on Siegel domains and complex hyperbolic spaces established.

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…

Explicit formulas for fractional GJMS operators on hyperbolic spaces and inequalities proved.

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, …

The paper proves Hardy and Rellich inequalities for submanifolds in Hadamard spaces.

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

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

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

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

Established a Hardy inequality on Finsler manifolds.

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

Proves inequalities on curved spaces with positive curvature.

Paper sharpens Hardy and Rellich inequalities on nonreversible Finsler manifolds.

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

Given a probability measure $μ$ supported on a convex subset $Ω$ of Euclidean space $(\mathbb{R}^d,g_0)$, we are interested in obtaining Poincaré and log-Sobolev type inequalities on $(Ω,g_0,μ)$. To this end, we change the metric $g_0$ to a more general Riemannian one $g$, adapted in a certain sense to $μ$, and perform…

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

Alternative proofs for various inequalities 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.

The paper examines eigenvalues and inequalities on Riemannian manifolds.

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…

Extends Riemannian geometry inequalities with sharper estimates.

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

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.

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

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

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…

Proves a conjecture about kernels on planar regions.

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

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

Frank and Lieb proved sharp Sobolev inequalities without rearrangements.

The study establishes bounds for Schrödinger operators on Riemannian manifolds.

We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n=2) leads to a direct proof of Onofri inequality on S^2.

Sharp inequalities and eigenvalue problems on Finsler manifolds with nonnegative Ricci curvature.

After works by Michael and Simon [10], Hoffman and Spruck [9], and White [14], the celebrated Sobolev inequality could be extended to submanifolds in a huge class of Riemannian manifolds. The universal constant obtained depends only on the dimension of the submanifold. A sort of applications to the submanifold theory a…

We prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying an inverse doubling volume condition. It enables us to obtain rigidity results for Ricci flat manifolds, generalizing earlier work of Bando, Kasue and Nakajima.

Uniform Poincaré inequalities established for various metric spaces.

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

We prove a Hardy inequality for uniformly elliptic operators subject to Dirichlet or mixed boundary conditions on domains $Ω$ with piecewiese smooth boundary in arbitrary Riemannian Manifolds (M, g). Employing an approach of E.B. Davies for the euclidean case, we show that it implies a sufficient geometric criterion un…

Uniform Poincaré inequalities on manifolds with bounded Ricci curvature.

Uniform rectifiability proven for sets with Poincaré inequalities.

Sharp HLS inequality on bounded domains with applications to curvature and isoperimetric constants.

Poincaré and Sobolev inequalities for differential forms on Heisenberg balls are derived.