We prove the stability of the affirmative part of the solution to the complex Busemann–Petty problem. Namely, if K and L are origin-symmetric convex bodies in mathbb Cn{{mathbb C}^n}, n = 2 or n = 3, ${varepsilon >0 }${varepsilon >0 } and Vol2n-2(KÇH) £ Vol2n-2(L ÇH) + e{{rm Vol}_{2n-2}(Kcap H) le {rm Vol}_{2n-2}(L cap H) + varepsilon} for any complex hyperplane H in mathbb Cn{{mathbb C}^n} , then (Vol2n(K))fracn-1n £ (Vol2n(L))fracn-1n + e{({rm Vol}_{2n}(K))^{frac{n-1}n}le({rm Vol}_{2n}(L))^{frac{n-1}n} + varepsilon} , where Vol2n is the volume in mathbb Cn{{mathbb C}^n} , which is identified with mathbb R2n{{mathbb R}^{2n}} in the natural way.
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机译：我们证明了复杂的Busemann-Petty问题解的肯定部分的稳定性。也就是说，如果K和L是mathbb C n {{mathbb C} ^ n}中的原点对称凸体，则n = 2或n = 3，则$ {varepsilon> 0} $ {varepsilon> 0}和Vol 2n-2 （KÇH）£Vol 2n-2 （LÇH）+ e {{rm Vol} _ {2n-2}（Kcap H） le {rm Vol} _ {2n-2}（L cap H）+ varepsilon}对于mathbb C n {{mathbb C} ^ n}中的任何复超平面H，然后（Vol 2n （K）） fracn-1n £（Vol 2n （L）） fracn-1n + e {（{rm Vol} _ {2n}（K））^ {frac {n-1} n} le（{rm Vol} _ {2n}（L））^ {frac {n-1} n} + varepsilon}，其中Vol 2n 是mathbb C n {{mathbb C} ^ n}中的体积，用mathbb R 2n {{mathbb R}标识^ {2n}}以自然的方式。
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