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- W2017008566 abstract "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 $${{mathbb C}^n}$$ , n = 2 or n = 3, $${varepsilon >0 }$$ and $${{rm Vol}_{2n-2}(Kcap H) le {rm Vol}_{2n-2}(L cap H) + varepsilon}$$ for any complex hyperplane H in $${{mathbb C}^n}$$ , then $${({rm Vol}_{2n}(K))^{frac{n-1}n}le({rm Vol}_{2n}(L))^{frac{n-1}n} + varepsilon}$$ , where Vol2n is the volume in $${{mathbb C}^n}$$ , which is identified with $${{mathbb R}^{2n}}$$ in the natural way." @default.
- W2017008566 created "2016-06-24" @default.
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- W2017008566 date "2011-04-14" @default.
- W2017008566 modified "2023-10-04" @default.
- W2017008566 title "Stability of volume comparison for complex convex bodies" @default.
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- W2017008566 doi "https://doi.org/10.1007/s00013-011-0254-1" @default.
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