关于三角形与点的一个不等式

涉及三角形与一个动点的不等式是一类有趣的几何不等式.在文献[1]中作者曾运用重要的"惯性极矩不等式"证明了下述不等式:对△ABC与平面上任一点P有PA2sinA/2+PB2sinB/2+PC2sinC/2≥3r2,(1)其中r为△ABC的内切圆半径.……     

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.     

若干几何不等式及相应的代数式

本文将建立涉及三角形平面上一动点 P的一组新的几何不等式 ,并利用三角形的重心坐标给出这些几何不等式的相应代数式 .这里 ,P点到三边和三顶点的距离都是带符号的 ,与 P点的重心坐标符号相一致 .有关三角形重心坐标的定义、定理参见文 [1 ].设△ ABC三内角∠ A,∠ B,∠ C的对边分别为 a,b,c.用 s,R,r,△分别表示△ ABC的半周长 ,外接圆半径 ,内切圆半径和面积 .以 ha,hb,hc,ra,rb,rc分别为相应边上的高和旁切圆半径 .∑ 表示循环求和 ,用 P( x,y,z)表示 P点关于坐标△ ABC的重心坐标 .1　仅含 (PD,PE,PF)的一组不等式众所周知 ,…     

关于二元不等式所表平面区域的判定

<正> 在二元函数的微积分学中经常要接触到平面区域概念,而平面区域又常用不等式表达出来。例如,中心在M_0(x_0,y_0)点半径为R的圆域D={(x,y)|(x-x_0)~2+(y-y_0)~2相似文献   

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.     

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.     

关于内接单形的不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间E~n中涉及n维单形Ω_n与其内接单形Ω′_n的几何不等式的问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径与高线的一类几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.     

关于曲率积分不等式的注记

本文主要研究平面卵形线的曲率积分不等式.利用积分几何中凸集的支持函数以及外平行集的性质,得到了Gage等周不等式与曲率的熵不等式的一个积分几何的简化证明;进一步地,我们得到了一个新的关于曲率积分的不等式.     

涉及单形内点的一个几何不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及Ωn维单形Ω'n与其内接单形Ωn以及Ωn中内点之间的几何不等式问题,建立了涉及单形Ωn及其内接单形Ω'n的外接球半径以及Ωn中内点到各侧面距离之间的一个几何不等式,并给出了它的应用.     

共球有限点集的一类几何不等式

本文建立了Ｅｎ中共球有限点集的一类几何不等式，作为其特例，可以得到ｎ维单形的外接球半径与其子单形外接球半径之间的关系．     

Conjugate harmonic functions and Clifford algebras

We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.     

A Refinement of the Discrete Wirtinger Inequality

In this paper, we obtain an improved discrete Wirtinger inequality associated with a nonlinear second order differential equation. We apply this result to prove a Bonnesen-style isoperimetric inequality for plane polygons and reinterpret the main theorem as a weighted exponential inequality.     

Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane

We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory.     

一个引入中间变量的一般非齐次核全平面Hilbert型积分不等式

应用实分析及权函数的方法,引入一些参数及中间变量,建立一个一般非齐次核全平面Hilbert型积分不等式的若干等价陈述.常数因子被证明是最佳的.作为应用,一个一般齐次核全平面Hilbert型积分不等式的若干等价陈述被导出.我们还考虑了一些特殊情况、算子表示及若干例子.     

Isoperimetric inequality in the Grushin plane

We prove a sharp isoperimetric inequality in the Grushin plane and compute the corresponding isoperimetric sets.     

The equivalence of Side-Angle-Side with Side-Side-Side and the general triangle inequality in the absolute plane

We show that if we start with an absolute plane, remove Side-Angle-Side as an axiom, and replace it with Side-Side-Side together with a weakened version of the triangle inequality as new axioms, then the new resulting axiom system is also an absolute plane. In particular, we show that Side-Angle-Side still holds in the new axiom system. In addition, we give a new proof of the two-circle theorem which does not depend on Side-Angle-Side, but instead uses Side-Side-Side and the weakened version of the triangle inequality.     

On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane

By using techniques of real analysis and weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the extended Hurwitz zeta function is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and some corollaries.

     

Hadamard type inequality for quasiconvex functions in higher dimensions

In this article we study a Hadamard type inequality for nonnegative evenly quasiconvex functions. The approach of our study is based on the notion of abstract convexity. We also provide an explicit calculation to evaluate the asymptotically sharp constant associated with the inequality over a unit square in the two-dimensional plane.     

On 3-syzygy and unexpected plane curves

Geometriae Dedicata - We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity...     

The Weighted Weak Type Inequality for the Strong Maximal Function

We prove the natural Fefferman-Stein weak type inequality for the strong maximal function in the plane, under the assumption that the weight satisfies a strong Muckenhoupt condition. This complements the corresponding strong type result due to Jawerth. It also extends the weighted weak type inequality for strong A₁ weights due to Bagby and Kurtz.