RECONSTRUCTION PROBLEMS OF CONVEX BODIES FROM EVEN L_(p)SURFACE AREA MEASURES  

作　　者：Juewei HU Gangsong LENG 胡珏伟;冷岗松(Department of Mathematics,Shanghai University,Shanghai,200444,China)

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai,200444,China

出　　处：《Acta Mathematica Scientia》2025年第1期126-142,共17页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(12171304).

摘　　要：We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.

关 键 词：reconstruction problem even L_(p)surface area measures spherical harmonic 

分 类 号：O17[理学—数学]