A generalization of the total mean curvature

a generalization of strong causality

در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...

Lipschitzian Mappings and Total Mean Curvature

For a smooth closed surface C in E3 the classical total mean curvature is defined by M(C) = ¿/(«i + k2) do(p), where kx, k2 are the principal curvatures at p on C. If C is a polyhedral surface, there is a well known discrete version given by M(C) = IE/,(w a,), where 1¡ represents edge length and a, the corresponding dihedral angle along the edge. In this article formulas involving differentials...

Total Mean Curvature and Closed Geodesics

The proofs and applications are based on a Riemannian version of Gromov’s non-squeezing theorem and classical integral geometry. Given a convex surface Σ ⊂ R and a point q in the unit sphere S we denote by UΣ(q) the perimeter of the orthogonal projection of Σ onto a plane perpendicular to q. We obtain a function UΣ on the sphere which is clearly continuous, even, and positive. Let us denote the...

Generalization of -Centroidal Mean and its Dual

In this paper, the generalized -centroidal mean and its dual form in 2 variables are introduced. Also, studied some properties and prove their monotonicity. Further, shown that various means are partic- ular cases of generalized $bf{alpha}$-centroidal mean.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form