YANG Liu, HE Bin-wu. Applications of a New Affine Invariant for Polytopes[J]. Applied Mathematics and Mechanics, 2008, 29(2): 247-252.
Citation: YANG Liu, HE Bin-wu. Applications of a New Affine Invariant for Polytopes[J]. Applied Mathematics and Mechanics, 2008, 29(2): 247-252.

Applications of a New Affine Invariant for Polytopes

  • Received Date: 2007-03-12
  • Rev Recd Date: 2007-11-21
  • Publish Date: 2008-02-15
  • Using the technique of combination extremum,it was obtained that the analytic expression of the affineinvariant functional,by Lutwak,Yang and Zhang recently introduced,defined on a specific subclass of origin-symmetric convex polytopes in n-dimensional Euclidean space,and an application of it to Minkowski problem for origin-symmetric convex polytopes was given.
  • loading
  • [1]
    Lutwak E,Yang D,Zhang G.A new affine invariant for polytopes and Schneider's projection problem[J].Trans Amer Math Soc,2001,353(5):1767-1779. doi: 10.1090/S0002-9947-01-02726-X
    [2]
    Marcus M,Lopes L.Inequalities for symmetric function and Hermitian matrices[J].Canad J Math,1957,9(2):305-312. doi: 10.4153/CJM-1957-037-9
    [3]
    Gluck H.The generalized Minkowski poblem in differential geometry in the large[J].Ann Math,1972,96(2):245-276. doi: 10.2307/1970788
    [4]
    Singer D.Preassigning curvature of polyhedra homeomorphic to the two-sphere[J].J Differential Geom,1974,9(4):633-638.
    [5]
    Gluck H.Manifolds with preassigned curvature—a suvey[J].Bull Amer Math Soc,1975,81(2):313-329. doi: 10.1090/S0002-9904-1975-13740-2
    [6]
    Lutwak E.The Brunn-Minkowski-Firey theory Ⅰ:Mixed volumes and the Minkowski problem[J].J Differential Geom,1993,38(1):131-150.
    [7]
    Lutwak E,Oliker V.On the regularity of solutions to a generalization of the Minkowski problem[J].J Differential Geom,1995,41(1):227-246.
    [8]
    Lamberg L,Kaasalainen M.Numerical solution of the Minkowski problem[J].J Comput Appl Math,2001,137(2):213-227. doi: 10.1016/S0377-0427(01)00360-0
    [9]
    Stancu A.The discrete planar L0-Minkowski problem[J].Adv Math,2002,167(1):160-174. doi: 10.1006/aima.2001.2040
    [10]
    Stancu A.On the number of solutions to the discrete two-dimensional L0-Minkowski problem[J].Adv Math,2003,180(1):290-323. doi: 10.1016/S0001-8708(03)00005-7
    [11]
    Umanskiy V.On solvability of two-dimensional Lp-Minkowski problem[J].Adv Math,2003,180(1):176-186. doi: 10.1016/S0001-8708(02)00101-9
    [12]
    Lutwak E,Yang D,Zhang G.On the Lp-Minkowski problem[J].Trans Amer Soc,2004,356(11):4359-4370. doi: 10.1090/S0002-9947-03-03403-2
    [13]
    He B W,Leng G S,Li K H.Projection problems for symmetric polytopes[J].Adv Math,2006,207(1):73-90. doi: 10.1016/j.aim.2005.11.006
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2274) PDF downloads(640) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return