Contraction Flow by Certain Curvature of Convex Hypersurfaces

In the following mixed tensors on the hypersurface M Rn+1 under consideration willbe denoted by T={ Tijkl} ,the induced metric by g={ gij} and the second fundamentalform by A={ hij} .We always sum overrepeated indices from1 to n and use brackets forthe inner product on M:〈Tijk,Sijk〉 =gisgjαgkβTijk Ssαβ,　 | T| 2 =〈Tijk,Tijk〉.Setrkl =gkαhαl,Sm(λ1 ,… ,λn) = i1<… 相似文献   

一个来自投资理论的抛物型Monge-Ampère方程初值问题

为寻找抛物型Monge-Ampere方程的初值问题VsVyy ryVyVyy-θV2y=0, Vyy<0,(s,y)∈[0,T)×R, V(T,Y)=g(y), g'(y)≥0,Y ∈R 满足最优投资理论要求的解,本文给出一个途径,并得到某些存在性结果.     

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From the theory of optimal investment in mathematical finance,the following initial valueproblem for a parabolic Monge—Ampere equation was derived in吣=0, (8,Y)∈[0,T)×R,where V=y(s,Y)is the unknown function,r,b,仃are given0,b—r>0,and in a typical case,the function g(y)is given by g(v)=1一e-,ky,constants with r≥0,盯>(2)where A iS a positive constant.The practice meaning of the above parameters and functionscan be found in Chapters 2 and 4 in[1】.From the mathematical point of view,the …     

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一个来自投资理论的抛物型Monge-Ampère方程初值问题

为寻找抛物型Monge-Ampere方程的初值问题{VsVyy+ryVyVyy-θ,Vyy＜0,(s,y)0∈[0,T]×,V(T,y)=g(y),g′(y)≥0,y＜R满足最优投资理论要求的解,本文给出一个途径,并得到某些存在性结果.