In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an...In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.展开更多
We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X...We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.展开更多
Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and...Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.展开更多
In this paper, we get a kinematic density formula for pairs of intersecting lines which has not yet been gotten in integral geometry by using the moving orthogonal frames method. And we obtain a kinematic formula of t...In this paper, we get a kinematic density formula for pairs of intersecting lines which has not yet been gotten in integral geometry by using the moving orthogonal frames method. And we obtain a kinematic formula of the intersection of the pairs of intersecting lines belonging to convex body K by using it.展开更多
In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fu...In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.展开更多
In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained i...In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.展开更多
kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space
In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the iso...In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the isometry group G in R2n. A sufficient condition for D0 contain D1 by using kinematic foundamatal formula and Poincare's formula in Rn is obtained.展开更多
基金supported in part by National Natural Science Foundation of China (Grant No.10971167)
文摘In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.
基金supported by National Natural Science Foundation of China (Grant No. 10971167)
文摘We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10671159)the Funds for Qualified Scientists and Technicians in Guizhou Province of China and Southwest University.
文摘Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.
基金the National Natural Science Foundation of China （No. 60074033）.
文摘In this paper, we get a kinematic density formula for pairs of intersecting lines which has not yet been gotten in integral geometry by using the moving orthogonal frames method. And we obtain a kinematic formula of the intersection of the pairs of intersecting lines belonging to convex body K by using it.
文摘In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.
基金Supported in part by National Natural Science Foundation of China(Grant Nos.11126324,11271302,11161007,11326073)
文摘In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.
基金supported by the National Natural Science Foundation of China(No.11271302)Chongqing Natural Science Foundation(No.cstc2011jj A00026)
文摘kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space
文摘In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the isometry group G in R2n. A sufficient condition for D0 contain D1 by using kinematic foundamatal formula and Poincare's formula in Rn is obtained.
