Bonnesen型Ros等周不等式

首先定义了欧氏平面上的Ros等周亏格,得到了Ros等周亏格与经典的等周亏格之间的关系,讨论了Bonnesen型Ros等周不等式.利用前人的一些著名的Bonnesen型不等式,我们得到了一些Bonnesen型Ros等周不等式.     

从积分几何的观点看几何不等式——纪念李国平院士吴新谋教授诞辰100周年

该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式.     

关于平面凸多边形的一个Bonnesen型不等式

本文探索了关于平面凸多边形的Bonnesen型不等式.利用分析方法,先构造一个解析函数的不等式,进而得到了一个关于平面凸多边形的Bonnesen型不等式.     

欧氏空间R3中的几个Bonnesen型不等式

本文研究欧氏空间R3中关于一个凸体的Bonnesen型不等式.利用包含测度的方法,获得了几个Bonnesen型不等式.     

几个关于极坐标的Bonnesen型不等式

本文研究了平面上C~2闭凸曲线的极坐标形式{O;ρ(θ)}.运用Bonnesen不等式的推广形式[1,2],得到关于ρ及ρ_θ的一些积分形式的Bonnesen型不等式,使得我们很容易得到等周不等式取等时的条件.     

平面两凸域的Bonnesen型对称混合不等式

本文利用积分几何中的Poincare运动公式和Blaschke运动公式估计平面上两域K_0和k_1的对称混合等周亏格△_2(K_0,K_1),得到了对称混合等周不等式和一些Bonnesen型对称混合不等式,其中一个不等式加强了Kotlyar的不等式.此外我们还得到了一些逆Bonnesen型对称混合不等式,其条件比著名的Bottema不等式的弱.     

R~n中的一个Bonnesen型不等式

研究了n维欧氏空间中凸体K的等周亏格的下界估计,即Bonnesen型不等式.首先加强了Lutwak中得到的关于凸体K的p-平均不等式,用此得到一个用凸体K的均质积分及调和均质积分表示的等周亏格的下界估计.     

平面Bonnesen型不等式的几点注记

本文研究了平面紧域的Bonnesen型不等式.利用紧域及其凸包的周长和面积得到一些新的Bonnesen型不等式以及两个用最大内切圆半径与最小外接圆半径表示的Bonnesen型不等式.     

两个新的Bonnesen型不等式

本文研究了Bonnesen型不等式.利用积分几何方法,得到了两个新的Bonnesen型不等式.     

几个与Ros等周亏格相关的逆Bonnesen型不等式

研究了平面卵形区域的Ros等周亏格问题,利用R~2中卵形区域的Ros定理及其加强形式,著名的等周不等式,给出R~2中卵形区域与Ros等周亏格相关的几个逆Bonnesen型不等式.     

Problems on polygons and Bonnesen-type inequalities

In this paper we are interested in some Bonnesen-type isoperimetric inequalities for plane n-gons in relation with the two conjectures proposed by P. Levy and X.M. Zhang.     

常曲率平面上的逆Bonnesen型不等式

利用积分几何中估计包含测度的思想给出常曲率平面上一些新的逆Bonnesen型不等式.这些不等式在欧氏平面上为著名的Bottema不等式的改进形式与新的逆Bonnesen型不等式.     

Bonnesen-style inequalities and pseudo-perimeters for polygons

In this paper, we establish some Bonnesen-style isoperimetric inequalities for plane polygons via an analytic isoperimetric inequality and an isoperimetric inequality in pseudo-perimeters of polygons.1991 Mathematics Subject Classification 51M10, 51M25,52A40,26D10.     

Gromov hyperbolic spaces and the sharp isoperimetric constant

In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and generalize theorems of Gromov, Papasoglu and others.     

Analytic inequalities,isoperimetric inequalities and logarithmic Sobolev inequalities

There is a simple equivalence between isoperimetric inequalities in Riemannian manifolds and certain analytic inequalities on the same manifold, more extensive than the familiar equivalence of the classical isoperimetric inequality in Euclidean space and the associated Sobolev inequality. By an isoperimetric inequality in this connection we mean any inequality involving the Riemannian volume and Riemannian surface measure of a subset α and its boundary, respectively. We exploit the equivalence to give log-Sobolev inequalities for Riemannian manifolds. Some applications to Schrödinger equations are also given.     

Two isoperimetric inequalities for the Sobolev constant

In this note, we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalizes an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.     

A Note on the Reverse Isoperimetric Inequality

In this paper, we derive an improved sharp version of a reverse isoperimetric inequality for convex planar curves of Pan and Zhang (Beitr?ge Algebra Geom 48:303?C308, 2007), with a simpler Fourier series proof. Moreover our result also confirm a conjecture by Pan et?al. (J Math Inequal (preprint), 2010). Furthermore we also present a stability property of our reverse isoperimetric inequality (near equality implies curve nearly circular).     

R3中卯形闭曲面的等周亏格的上界的注记

利用R^3中卵形结果的高斯曲率不等式以及著名的等周不等式,将R^3中卵形闭曲面的高斯曲率K应用到空间曲面的等周亏格的上界估计中,得到了R^3中卵形闭曲面的等周亏格的一个新的上界,并给出其简单证明．     

Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator

 We establish, by simple semigroup arguments, a Lévy–Gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature. Oblatum 19-VI-1995