http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
채영도,이영수 호남수학회 2012 호남수학학술지 Vol.34 No.3
In this paper, we prove that if K is a convex body in En and Ei and Eo are inscribed ellipsoid and circumscribed ellipsoid of K respectively with Ei = Eo, then h ()np +1in !2n V (K)V ( pK) h 1np +1in !2n : Lutwak and Zhang[6] proved that if K is a convex body, !2n = V (K)V ( pK) if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.
LOWER BOUND OF LENGTH OF TRIANGLE INSCRIBED IN A CIRCLE ON NON-EUCLIDEAN SPACES
채영도,이영수 호남수학회 2012 호남수학학술지 Vol.34 No.1
Wetzel[5] proved if is a closed curve of length L in En, then lies in some ball of radius [L=4]. In this paper, we gener-alize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.
Tubes in singular spaces of nonpositive curvature
채영도,이두한 대한수학회 2006 대한수학회지 Vol.43 No.5
In this paper, we estimate area of tube in a CBA(0)-space withextendible geodesics. As its application, we obtain an upper boundof systole in a nonsimply connected space of nonpositivecurvature. Also, we determine a relative growth of a ball in aCBA(0)-space to the corresponding ball in Euclidean plane.
A geometric inequality on a compact domain in $\mathbb R^{n}$
채영도,조용승 대한수학회 2018 대한수학회보 Vol.55 No.1
In this paper, we study some topological structure of a compact domain in $\mathbb R^{n}$ in terms of the curvature conditions and develop a geometric inequality involving the volume and the integral of mean curvatures over the boundary of the compact domain.
Integral formulas on the unit sphere
Chai, Young-Doo,Lee, Young-Soo 성균관대학교 기초과학연구소 1995 論文集 Vol.46 No.1
L.A. Santalo는 [6]에서, Unit Sphere상에서 Crofton's formula를 일반화시키고 여러 가지 공식들을 얻었다. 본 논문에서는 Unit Sphere상에서 Convex 집합들에 관한 density를 정의하고 그것을 이용해서 Convex 집합들에 관련 된 여러 공식들을 얻었다. 그리고 응용으로서, Sphere상에서의 부등식을 얻었다.
Lower Bound for Total Mean Curvature of Quasi Convex Sets in R^n
Chai, Young-Doo 성균관대학교 기초과학연구소 1988 論文集 Vol.39 No.1
In this paper we have a lower bound for a total mean curvature of quasi convex sets which are generaliyed convex sets in R^n. In fact we develop better lower bound for total mean curvature of convex sets in R^n than lower bound developed by santalo in some sence.