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1.
We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in
n
. We first estimate the kinematic formula for the total scalar curvature D
0gD
1
Rdv of then–2 dimensional intersection submanifold D
0gD
1. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in
n
(4). Forn=4, we directly obtain another sufficient condition in 4. 相似文献
2.
In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo's results. 相似文献
3.
This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in R~2 implies the convergence of the sequence of the corresponding origin-symmetric convex bodies in the Hausdorff metric. 相似文献
4.
In this paper, a dual Orlicz–Brunn–Minkowski theory is presented. An Orlicz radial sum and dual Orlicz mixed volumes are introduced. The dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality are established. The variational formula for the volume with respect to the Orlicz radial sum is proved. The equivalence between the dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality is demonstrated. Orlicz intersection bodies are defined and the Orlicz–Busemann–Petty problem is posed. 相似文献
5.
6.
Zhou Jiazu 《数学学报(英文版)》1990,6(4):327-333
In this paper, we continue the discussion of the conjecture which says that infinitesimal II-isometry of surface is infinitesimal I-isometry, i.e., infinitesimally rigid. We have some invariants by means of which some integral formulas are worked out. As an application to these integral formulas, we get some results on infinitesimal II-isometry of closed surface. The theorems proved are just more or less obvious generalizations of known results. 相似文献
7.
周家足 《数学物理学报(B辑英文版)》2011,31(2):361-366
Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere. 相似文献
8.
Science China Mathematics - The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space ?nwith smaller central hyperplane sections necessarily have smaller volumes.... 相似文献
9.
Lutwak et al.(2010) established the Orlicz centroid inequality for convex bodies and conjectured that their Orlicz centroid inequality could be extended to star bodies. Zhu(2012) confirmed the conjectured Lutwak, Yang and Zhang(LYZ) Orlicz centroid inequality and solved the equality condition for the case that φis strictly convex. Without the condition that φ is strictly convex, this paper studies the equality condition of the conjectured LYZ Orlicz centroid inequality for star bodies. 相似文献
10.
By using the moving frame method, the authors obtain a kind of
asymmetric kinematic formulas for the total mean curvatures of
hypersurfaces in the $n$-dimensional Euclidean space. 相似文献