共查询到20条相似文献,搜索用时 15 毫秒
1.
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. 相似文献
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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. 相似文献
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In this note we will present a stability property of the reverse isoperimetric inequality newly obtained in [S.L. Pan, H. Zhang, A reverse isoperimetric inequality for convex plane curves, Beiträge Algebra Geom. 48 (2007) 303-308], which states that if K is a convex domain in the plane with perimeter p(K) and area a(K), then one gets , where denotes the oriented area of the domain enclosed by the locus of curvature centers of the boundary curve ∂K, and the equality holds if and only if K is a circular disc. 相似文献
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平面Bonnesen型不等式 总被引:9,自引:1,他引:9
将用积分几何方法给出平面等周不等式以及Bonnesen型不等式,平面区域D的面积、周长、最大内接园半径及最小外接园半径的一些几何不等式的简单证明. 相似文献
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In this short note we will give another simple and elementary proof of the classical isoperimetric inequality in the Euclidean plane. 相似文献
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Summary The discrete isoperimetric problem is to determine the maximal area
polygon with at most <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource
Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>k$ vertices and of a given
perimeter. It is a classical
fact that the unique optimal polygon on the Euclidean plane is the regular one.
The same statement for the hyperbolic plane was proved by K\'aroly Bezdek [1]
and on the sphere by L\'aszl\'o Fejes T\'oth [3]. In the present paper we
extend the discrete isoperimetric inequality for ``polygons' on the three
planes of constant curvature bounded by arcs of a given constant geodesic
curvature. 相似文献
9.
Itai Benjamini Simi Haber Michael Krivelevich Eyal Lubetzky 《Random Structures and Algorithms》2008,32(1):101-114
The isoperimetric constant of a graph G on n vertices, i(G), is the minimum of , taken over all nonempty subsets S ⊂ V (G) of size at most n/2, where ∂S denotes the set of edges with precisely one end in S. A random graph process on n vertices, , is a sequence of graphs, where is the edgeless graph on n vertices, and is the result of adding an edge to , uniformly distributed over all the missing edges. The authors show that in almost every graph process equals the minimal degree of as long as the minimal degree is o(log n). Furthermore, it is shown that this result is essentially best possible, by demonstrating that along the period in which the minimum degree is typically Θ(log n), the ratio between the isoperimetric constant and the minimum degree falls from 1 to , its final value. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008 相似文献
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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. 相似文献
12.
Sufficient conditions for one domain to contain another in a space of constant curvature 总被引:4,自引:0,他引:4
Jiazu Zhou 《Proceedings of the American Mathematical Society》1998,126(9):2797-2803
As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space , -sphere , hyperbolic space (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space , or a -sphere or a hyperbolic space .
13.
In this paper, we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface $ \mathbb{X} $ ∈ of constant curvature ∈, that is, an isoperimetric deficit upper bound of the convex domain in $ \mathbb{X} $ ∈ . The result is an analogue of the known Bottema’s result of 1933 in the Euclidean plane $ \mathbb{E} $ 2. 相似文献
14.
设K_k(k=i,j)为欧氏平面R~2中面积为A_k,周长为P_k的域,它们的对称混合等周亏格(symmetric mixed isoperimetric deficit)为σ(K_i,K_j)=P_i~2P_j~2-16π~2A_iA_j.根据周家足,任德麟(2010)和Zhou,Yue(2009)中的思想,用积分几何方法,得到了两平面凸域的Bonnesen型对称混合不等式及对称混合等周不等式,给出了两域的对称混合等周亏格的一个上界估计.还得到了两平面凸域的离散Bonnesen型对称混合不等式及两凸域的对称混合等周亏格的一个上界估计,并应用这些对称混合(等周)不等式估计第二类完全椭圆积分. 相似文献
15.
By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater than 1. 相似文献
16.
Let be two convex compact subsets of the hyperbolic space with smooth boundary. It is shown that the total curvature of the hypersurface is larger than the total curvature of .
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We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface $\mathbb{X}_\varepsilon ^2$ of constant curvature ? via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema’s result in the Euclidean plane $\mathbb{E}^2$ . 相似文献
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We prove the uniqueness for the solutions of the singular nonlinear PDE system:
(1) |
In the special case when and , we classify all the solutions and thus obtain the best constant in the corresponding weighted Hardy-Littlewood-Sobolev inequality.
20.
By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional
hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater
than 1 相似文献