# Dvoretzky Type Theorems for Multivariate Polynomials and Sections of Convex Bodies

@article{Dolnikov2011DvoretzkyTT, title={Dvoretzky Type Theorems for Multivariate Polynomials and Sections of Convex Bodies}, author={V. Dol'nikov and R. Karasev}, journal={Geometric and Functional Analysis}, year={2011}, volume={21}, pages={301-318} }

In this paper we prove the Gromov–Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $${\mathbb{R}^{n}}$$, and improve bounds on the number n(d, k) in the analogous conjecture for odd degrees d (this case is known as the Birch theorem) and complex polynomials.We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in… CONTINUE READING

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