摘要
利用单形的"偏正"度量与几何不等式理论,研究欧氏空间En中关于n维单形的SalleeAlexander不等式与Veljan-Korchmaros不等式的稳定性,利用cscθ≥1的性质,获得它们新的稳定性版本,将原有的稳定性版本推广为对(n维单形Ω,τ∈[2,n],有(W(Ω))-2 n2-1)≥(cscθ)1/(n-1)2[βn(n+1)n+1/n/n(n!)2/nV-2/n]n2-1+λ(n,τ)·δ(Ω,Ω)和(W(Ω))-2(n2-1)≥(cscθ)1/(n-1)2(βnR-2)n2-1+λ(n,τ)·δ(Ω,Ω),证明它们是稳定的,推广了这些不等式得出了相应的推论。
By using the deviation regular metric and theory of geometric inequalities as a simplex sions of Sallee - Alexander inequality and Veljan - Kochmaros inequality for an n - simplex the stability ver- in the Euclidean space En were studied. With the characteristic being csc0 〉 1, the new stability versions of these inequalities were obtained. For n n -simplex in the Euclidean space E", the inequalities (W(Ω))-2 n2-1)≥(cscθ)1/(n-1)2[βn(n+1)n+1/n/n(n!)2/nV-2/n]n2-1+λ(n,τ)·δ(Ω,Ω)和(W(Ω))-2(n2-1)≥(cscθ)1/(n-1)2(βnR-2)n2-1+λ(n,τ)·δ(Ω,Ω), , were acquired, which are proved stable and the relative theories are gotten with their generalization
出处
《安徽理工大学学报(自然科学版)》
CAS
2017年第1期81-86,共6页
Journal of Anhui University of Science and Technology:Natural Science
基金
安徽省自然科学重点科研项目(KJ2015A351)