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

We prove an improved version of Poincar\'e-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Hardy type inequality with an improved constant (than the…

Let G be a k-step Carnot group. We prove an isoperimetric-type inequality for compact C^2-smooth immersed hypersurfaces with boundary, involving the horizontal mean curvature of the hypersurface. This generalizes an inequality due to…

We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension $\geq 2$ and arbitrary co-dimension, provided they are initially close to a flat plane.

We prove a sharp isoperimetric inequality for measured Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of…

We extend the results of B. Minemyer by showing that any indefinite metric polyhedron (either compact or not) with the vertex degree bounded from above admits an isometric simplicial embedding into a Minkowski space of the lowest possible…

We give an alternative proof of the Michael-Simon-Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension $2$.

We combine conditions found in [Wh] with results from [MPR] to show that quasi-isometries between uniformly discrete bounded geometry spaces that satisfy linear isoperimetric inequalities are within bounded distance to bilipschitz…

Klartag's needle decomposition technique enables one to obtain strong isoperimetric inequalities on Riemannian manifolds other than the classical known examples. As a result, in this paper, we obtain sharp isoperimetric inequalities for…

We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly positive definite (0, 2)-tensor fields on compact submanifolds with or without boundary in Riemannian manifolds with nonnegative sectional curvature by the…

We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric…

Elementary proofs of sharp isoperimetric inequalities on a normed space $(\mathbb{R}^n,||\cdot||)$ equipped with a measure $\mu = w(x) dx$ so that $w^p$ is homogeneous are provided, along with a characterization of the corresponding…

In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski…

In this paper, we prove an isoperimetric inequality for the domain of dependence of a finite lightcone in the Minkowski spacetime of dimension greater than or equal to 3. The inequality involves two quantities: the volume of the domain of…

We prove Michael-Simon type Sobolev inequalities for $n$-dimensional submanifolds in $(n+m)$-dimensional Riemannian manifolds with nonnegative $k$-th intermediate Ricci curvature by using the Alexandrov-Bakelman-Pucci method. Here…

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…

We show a reverse isoperimetric inequality within the class of relative outer parallel bodies, with respect to a general convex body $E$, along with its equality condition. Based on the convexity of the sequence of quermassintegrals of…

We prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifold with nonnegative sectional curvature of arbitrary dimension and codimension, while the ambient manifold needs to…

Using the ABP-method as in a recent work by Brendle, we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian manifold with asymptotically nonnegative curvature. These…

In this paper, we prove a Pr\'ekopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality. It extends an inequality proved by Das Gupta [8] and Klartag [16], and thus recovers the Pr\'ekopa-Leindler inequality. In addition, we…

For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also…