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Title of Journal: Arch Math

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Abbravation: Archiv der Mathematik

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SP Birkhäuser Verlag Basel

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DOI

10.1002/chem.201406094

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1420-8938

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Stability of volume comparison for complex convex

Authors: Alexander Koldobsky
Publish Date: 2011/04/14
Volume: 97, Issue: 1, Pages: 91-98
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Abstract

We prove the stability of the affirmative part of the solution to the complex Busemann–Petty problem Namely if K and L are originsymmetric convex bodies in mathbb Cn n = 2 or n = 3 varepsilon 0 and rm Vol 2n2Kcap H le rm Vol 2n2L cap H + varepsilon for any complex hyperplane H in mathbb Cn then rm Vol 2nKfracn1nlerm Vol 2nLfracn1n + varepsilon where Vol2n is the volume in mathbb Cn which is identified with mathbb R2n in the natural way

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  1. On an asymptotically autonomous system with Tikhonov type regularizing term
  2. Inverse positivity for general Robin problems on Lipschitz domains
  3. Gromov hyperbolicity of negatively curved Finsler manifolds
  4. Courbes planes à nœuds et à cusps
  5. On one-sided strong Arens irregularity
  6. Null controllability with constraints on the state for the linear Korteweg-de Vries equation
  7. Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions
  8. A problem of Carlitz and its generalizations
  9. Distribution of the coefficients of modular forms and the partition function
  10. The abstract Dirichlet problem for continuous vector-valued functions
  11. Lower bounds on the number of maximal subgroups in a finite group
  12. Some properties of Gurarii's modulus of convexity
  13. On the generalization of Faltings’ Annihilator Theorem
  14. On the identities defining a quadratic Jordan division algebra
  15. Abelian Carter subgroups in finite permutation groups
  16. On trace ideal weighted composition operators on weighted Fock spaces
  17. On curves with all Weierstrass points of maximal weight
  18. Bounds for the probability of generating the symmetric and alternating groups
  19. A characterization of the  -genus as a linear combination of Pontrjagin numbers
  20. Complemented ideals in $$A({\mathbb{R}}^{d})$$ of algebraic curves
  21. Power-free values of polynomials
  22. Gradient blowup rate for a viscous Hamilton–Jacobi equation with degenerate diffusion
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