arXiv research

In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.

Sharp inequality on Siegel domain involving weighted norms and sub-Laplacian.

We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove that the $\log^\dd$-Sobolev inequality with $\dd\in (1,2)$ implies the $L^{2/(2-\d…

Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.

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.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

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

The paper proves inequalities under Bakry-Émery-Ricci curvature bounds.

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

Proves inequality linking function deviation to gradient norm on compact manifolds.

We refine and generalize several interpolation inequalities bounding the $L^p$ norm of a probability density with respect to the reference measure $μ$ by its Sobolev norm and the Kantorovich distance to $μ$ on a smooth weighted Riemannian manifold satisfying $CD(0, \infty)$ condition.

The study improves Bochner inequality on Finsler manifolds to derive important inequalities.

The paper proves gradient estimates for a weighted p-Laplacian equation on Riemannian manifolds.

Finite time for subsolutions on Riemannian manifolds proved.

The paper proves local rigidity theorems for scalar curvature and related inequalities.

We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted Riemannian manifolds satisfying $\mathrm{Ric}_{\infty} \ge K>0$. Assuming equality holds, we show that the $1$-dimensional Gaussian space is necessarily split off, similarly to the rigidity results of Cheng--Zhou on the spectral gap …

Under a spectral assumption on the Laplacian of a Poincaré--Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order $2γ\in(0,2)$ or $2γ\in(2,4)$ and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption…

We define a very general "parametric connect sum" construction which can be used to eliminate isolated conical singularities of Riemannian manifolds. We then show that various important analytic and elliptic estimates, formulated in terms of weighted Sobolev spaces, can be obtained independently of the parameters used …

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.

Sharp inequality found on three-balls for fourth order Sobolev traces.

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…

New Sobolev inequalities on Kähler manifolds with positive Ricci curvature.

The paper proves inequalities for varifolds on Riemannian manifolds.

The purpose is to study the CR-manifold with a contact structure conformal to the Heisenberg group. In our previous work \cite{WY}, we have proved that if the $Q'$-curvature is nonnegative, and the integral of $Q'$-curvature is below the dimensional bound $c_1'$, then we have the isoperimetric inequality. In this paper…

Characterizes Schrödinger operator boundedness on weighted Riemannian manifolds.

Paper connects Fenchel-Willmore and Sobolev inequalities for submanifolds in curved spaces.

Explains optimal functional inequalities, focusing on Sobolev and fractional Sobolev.

The paper proves inequalities on Finsler manifolds under Ricci curvature bounds.

Log Sobolev and Michael Simon inequalities for tensor fields on curved manifolds.

The paper proves a Harnack inequality for heat equations on Finsler metric measure manifolds.

Alternative proof of Michael-Simon-Sobolev inequality using optimal transport.

Sharp Sobolev and Michael-Simon inequalities on curved manifolds.

Study noncommutative Sobolev inequalities using quantum state metrics.

In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to extend the author's results on the $W^{1,2}$ Sobolev inequality along the Ricci flow …

Proves Sobolev inequality on manifolds with specific curvature properties.

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…

Proves new Sobolev inequalities for submanifolds in manifolds with nonnegative intermediate Ricci curvature.

Paper introduces new fractional Dirac operator and Q-curvature.

New Sobolev inequalities found for curved spaces.

The paper examines stability of Sobolev inequalities on manifolds with Ricci curvature bounds.

Improved CR Sobolev inequalities on CR sphere established.

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

The paper improves CR Sobolev inequalities and classifies minimizers.

Upper bounds on constants for Brownian motion with sticky boundary.

The isoperimetric inequality and related inequalities are explored.

Sharp inequalities on curved spaces with bounded curvature.

We prove a sharp logarithmic Sobolev inequality which holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature.

Study shows how close functions are to optimal in Riemannian manifolds.