Related papers: Moser-Trudinger inequality on conformal discs

We establish a supercritical Trudinger-Moser type inequality for the $k$-Hessian operator on the space of the $k$-admissible radially symmetric functions $\Phi^{k}_{0,\mathrm{rad}}(B)$, where $B$ is the unit ball in $\mathbb{R}^{N}$. We…

A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a…

In this article, we study the connection between the fractional Moser-Trudinger inequality and the fractional $\left(\frac{kp}{p-1},p\right)$-Poincar\'e type inequality for any Euclidean domain and discuss the sharpness of this inequality…

Moduli spaces of holomorphic disks in a complex manifold Z, with boundaries constrained to lie in a maximal totally real submanifold P, have recently been found to underlie a number of geometrically rich twistor correspondences. The purpose…

In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^{m}(\Omega)$, where $\Omega$ is any bounded, smooth, open subset of $\mathbb{R}^{2m}$, $m\ge 1$. Moreover, we extend…

We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger…

In this paper, we first establish the quantitative properties for positive solutions to the Moser-Trudinger equations in the two-dimensional Poincar\'e disk $\mathbb{B}^2$: \begin{equation*}\label{mt1} \left\{ \begin{aligned}…

In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball…

This paper is devoted to study the sharp Moser-Trudinger type inequalities in whole space $\mathbb R^N$, $N \geq 2$ in more general case. We first compute explicitly the \emph{normalized vanishing limit} and the \emph{normalized…

We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \text{rad}}(B_R^N)\,(p<N)$. Our results give a revision of an…

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result…

In this paper, we will establish the best constants for certain classes of weighted Moser-Trudinger inequalities on the entire Euclidean spaces $\mathbb{R}^N$. We will also prove the existence of maximizers of these sharp weighted…

We show that a length-minimizing disk inherites the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.

This is a continuation of our previous work [13]. Let $(\Sigma,g)$ be a closed Riemann surface, where the metric $g$ has conical singularities at finite points. Suppose $\mathbf{G}$ is a group whose elements are isometries acting on…

We establish a Trudinger-Moser type inequality with a Tintarev-type constraint in fractional-dimensional spaces and prove the existence of maximizers in the critical regime. Our results provide a refinement of those in (Calc. Var. 52…

We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to…

We prove that for every metric on the torus with curvature bounded from below by -1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the induced metric on the boundary is the given metric. The proof…

This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this…

Let $(M,g)$ be a 2-dimensional compact Riemannian manifold. In this paper, we use the method of blowing up analysis to prove several Moser-Trdinger type inequalities for vector bundle over $(M,g)$. We also derive an upper bound of such…

We prove that a 3-dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by the metric induced on its boundary. Furthemore, any hyperbolic metric on the torus with cone singularities of positive curvature can be…