Related papers: Aubin type almost sharp Moser-Trudinger inequality…

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in…

Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to $L^\infty$. It is well known that the original form of the inequality with the sharp exponent (proved…

In this paper, we establish the bounds of sharp Trudinger-Moser inequalities on Euclidean space. Let $B$ be a ball in $\mathbb{R}^n$ and $$TM(B)=\sup_{u\in{W_{0}^{1,n}(B)},\|\nabla…

This paper is devoted to a kind of rearrangement of functions on CD(k,n)-spaces, which satisfy a Polya-Szeg\"o type inequality. We use this rearrangement to prove the validity of a Moser-Trudinger type inequality on a wide class of metric…

In this article, we introduce an analogous problem to Yamabe type problem considered by Case, J., which generalizes the Escobar-Riemann mapping problem for smooth metric measure spaces with boundary. The last problem will be called…

Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound.…

We extend several Cheeger-type isoperimetric bounds for convex sets in Euclidean space, due to Bobkov and Kannan-Lov\'asz-Simonovits, to Riemannian manifolds having non-negative Ricci curvature. In order to extend Bobkov's bound, we require…

In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform…

This paper is devoted to Hardy inequalities concerning distance functions from submanifolds of arbitrary codimensions in the Riemannian setting. On a Riemannian manifold with non-negative curvature, we establish several sharp weighted Hardy…

Inspired by [1, 13], we prove Michael-Simon type inequalities for smooth symmetric uniformly positive define (0, 2)-tensor fields on compact submanifolds in Euclidean space by the Alexandrov-Bakelman-Pucci (ABP) method.

We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.

In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the…

We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar\'e's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also…

This paper is devoted to the Moser-Trudinger inequality on smooth riemanniansurfaces. We establish that the constants involved can be chosen to depend on only 3parameters, which are the systole, isoperimetric constant and curvature of the…

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type $\displaystyle Lu:=-r^{-\theta}(r^{\alpha}\vert…

Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with…

The theory of sharp geometric inequality in $\mathbb{R}^n$ and inside convex cone has been well-developed, much less known for sharp capillary geometric inequality outside convex domain. Recently, Fusco-Julin-Morini-Pratelli \cite{FJMP}…

In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous works, we remove the Ricci curvature condition and…

We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential…

We first establish a family of sharp Caffarelli-Kohn-Nirenberg type inequalities on the Euclidean spaces and then extend them to the setting of Cartan-Hadamard manifolds with the same best constant. The quantitative version of these…