The total curvature of C2 curves embedded in an arbitrary Riemannian manifold is shown to be the limit of the curvatures of inscribed geodesic polygons. The formula for the total curvature of a curve as the least upper bound of curvatures of inscribed geodesic polygons holds for a manifold of...
6.3.2. Total Curvature. 在本小节中,我们将探讨有关平面曲线(signed curvature of a plane curve)有符号曲率的一个有趣结果。我们首先介绍:定义6.29(闭合曲线Closed Curves)。如果 γ(0)=γ(L) ,则弧长参数化平面曲线( arc-length parametrized plane curve) γ...
Since angles subtended by pairs of geodesics are independent of the choice of model spaces [8], it follows that the total curvature of a curve depends only locally on the metric, and not on the bound K. In [4], Alexander and Bishop defined total curvature for curves in CAT(0) spaces,...
We study the infimum of the total mixed curvature in a family of open curves whose endpoints and principal normal vectors at the endpoints are prescribed. In our previous works, we studied similar problems for the total absolute curvature, which is the length of the spherical curve defined by ...
Total (absolute) curvature is defined for any curve in a metric space. Its properties, finiteness, local boundedness, Lipschitz continuity, depending whether there are satisfied or not, permit a classification of curves alternative to the classical regularity classes. In this paper, we are mainly ...
If we know a plane curve $$\\gamma \\colon [a,b]o \\mathbb {R}^2$$\nγ\n:\n[\na\n,\nb\n]\n→\nR\n2\nnear its end points, we know its total curvature $$\\int \\_a^b \\kappa \\,ds$$\n∫\na\nb\nκ\nd\ns\nup to an integer multiple of $$2\\pi $$\n2\n...
1) total curvature 整体曲率1. Surface denoising based on total curvature and variational level set methods; 整体曲率变分水平集方法的曲面去噪模型2) general yield curve 整体收益率曲线 1. Using experiences from the US and HK markets,the paper proposes to take Shibor as the central pricing ...
1.INTRODUCTION:TOTALCURVATURE ThecelebratedF´ary-MilnortheoremstatesthatacurveinR n oftotalcurvature atmost4πisunknotted[Fa],[Mi].Inthepresentpaper,Ishallemphasizethe knottingdimensionn=3.Asakeystepinhis1950proof,JohnMilnorshowed thatforasmoothJordancurveΓinR 3 ,thetotalcurvatureequalsone-halfthe in...
Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a ...
Based on early work in the nineteenth century of Laplace, Young, and Plateau (e.g., Reference 94), a general expression for capillary pressure, Pc, as a function of interfacial tension, σ, and curvature of the interface is [19]: (1.74)Pc=σ1r1+1r2 where r1 and r2 are the principa...