相关论文: An Isoperimetric-Type Inequality for Spacelike Sub…

We give a new proof of the almost sharp Moser-Trudinger inequality on compact Riemannian manifolds based on the sharp Moser inequality on Euclidean spaces. In particular we can lower the smoothness requirement of the metric and apply the…

In this note, we obtianed hypercontractive inequalities between different weighted Bergman spaces. In addition, we establish Nikol'ski\u{\i}-type inequalities for weighted Bergman spaces with optimal constants.

In this paper, we study the Dirichlet problem associated to the maximal surface equation. We prove the uniqueness of bounded solutions to this problem in unbounded domain in R^2.

If a pair of subsets of two-dimensional Euclidean space nearly achieves equality in the Brunn-Minkowski inequality, in the sense that the measure of the associated sumset is nearly equal to the lower bound provided by the inequality, then…

We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\pi$. Here strong spacelike means that the tangent…

In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces. Our new definition based only on distance properties allows us also to deal with discrete spaces.…

The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free…

Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.

In the paper we establish an optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers in the Euclidean space, which generalizes a recent result of Brendle \cite{Brendle22} for closed self-shrinkers.…

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.

In this paper, the mixed Lp-surface area measures are defined and the mixed Lp Minkowski inequality is obtained consequently. Furthermore, the mixed Lp projection inequality for mixed projection bodies is established.

We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure…

In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with ${\rm Ric}\geq-ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to…

This paper announces the discovery of an isoperimetric inequality for the area of plane regions defined by binary forms. This result has been applied subsequently in the enumeration of solutions to the Thue inequality and, given its…

We prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is based on barrier constructions and local a priori estimates.

We consider Finsler submanifolds $M^n$ of nonnegative Ricci curvature in a Minkowski space $\mathbb{M}^{n+p}$ which contain a line or whose relative nullity index is positive. For hypersurfaces, submanifolds of codimension two or of…

We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the…

We establish Willmore-type inequalities for bounded domains in complete non-compact Riemannian manifolds, under either asymptotic or integral Ricci curvature bounds. Those results recover a recent inequality of Jin-Yin arXiv:2402.02465.

This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski…