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...
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 ...
On the total absolute curvature of closed curves in spheres 来自 Semantic Scholar 喜欢 0 阅读量: 15 作者: E Teufel 摘要: The total absolute curvature of a closed curve in a Euclidean space is always greater or equal to 2 (Fenchel's inequality,1929, [3], [1], [13]); especially ...
completeembeddedminimalsurfacesoffinitetotalcurvatureofgenuszerowiththree,four,orfiveends,and,exceptfortheplane,anembeddedcompleteminimalsurfaceoffinitetotalcurvaturehadatleasttwoends.Recently,R.Schoen[5]hasprovedthattheonlycompleteembeddedminimalsurfaceofanygenuswithfinitetotalcurvatureandtwoendsisthecatenoid.The...
Our proof relies on fundamental lemmas about the total curvature of curves that are packed in certain ways: If a long smooth curve A with arclength L is contained in a solid ball of radius ρ, then the total curvature of K is at least proportional to L / ρ. If A connects concentric ...
In the fifth chapter, the structure of distance circles and the cut locus of a Jordan curve in a complete open finitely connected Riemannian 2-manifold is investigated under the assumption that the manifold admits a total curvature. In the sixth chapter, we see that the total curvature of a ...
Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the ... J Gravesen,M Ungstrup - 《Advances in Computational Mathematics》 被引量: 50发表: 2002年 Evaluation of shape variability of stallion sperm...
We found a decrease of difficulty and an increase of efficiency during the first 20 cases and a more consistent execution after the initial five cases. Estimating the correct osteotomy level and stem curvature was often difficult, which resulted in a variable stem position. Radiologic analysis ...
To overcome the discrepancy between the implant and the curvature of the distal femoral shaft, especially concerning the unique characteristics of the geriatric Asian femur, femoral stem design could be adapted to incorporate a radius of curve. Through computational simulation of the modified femoral ...