Related papers: A sharp lower bound on the polygonal isoperimetric…

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…

The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle brings also quantitative…

Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of…

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

Sharp reverse affine isoperimetric inequalities for asymmetric Wulff shapes and their polars are established, along with the characterization of all extremals. These new inequalities have as special cases previously obtained simplex…

Let $ M^n$ be a closed immersed minimal hypersurface in the unit sphere $\mathbb{S}^{n+1}$. We establish a special isoperimetric inequality of $M^n$. As an application, if the scalar curvature of $ M^n$ is constant, then we get a uniform…

We prove a relative isoperimetric inequalities for Lagrangian half disks in $\mathbb{C}^2$ with respect to a Lagrangian plane, or a complex plane, or a union of any two of Lagrangian or complex planes that intersect transversally at the…

We provide a new characterization of the logarithmic Sobolev inequality.

The Euclidean concentration inequality states that, among sets with fixed volume, balls have $r$-neighborhoods of minimal volume for every $r>0$. On an arbitrary set, the deviation of this volume growth from that of a ball is shown to…

We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under…

We prove Ptolemaean Inequality and Ptolemaeus' Theorem in the closure complex hyperbolic plane endowed with the Cygan metric.

It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter…

We prove an sharp anisotropic isoperimetric inequality for a domain outside an Euclidean ball in $\mathbb{R}^n$ for $n\geq 2$. The proof applies the ABP method to a Neumann boundary value problem.

We present several sharp upper bounds and some extension for product operators. Among other inequalities, it is shown that if , , are non-negative continuous functions on such that , , then for all non-negative operator monotone decreasing…

Cheeger inequality is a classical result emerging from the isoperimetric problem in the field of geometry. In the graph theory, a discrete version of Cheeger inequality was also studied deeply and the notion was further extended for higher…

We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.

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 give a short proof of a reverse isoperimetric inequality due to Y. Groman and J. P. Solomon.

We obtain the sharp lower bound for the uniform norm of the orthogonal polynomials in the Steklov class. We also prove the sharp estimates for the polynomial entropy in this class.