Zero sets of polynomials in several variables |
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Authors: | R M Aron P Hájek |
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Institution: | (1) Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA;(2) Mathematical Institute of the Czech Academy of Science, Žitná 25, CZ-Praha, Czech Republic |
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Abstract: | Let
, where n is odd. We show that there is an integer N = N(k, n) such that for every n-homogeneous polynomial
there exists a linear subspace
, such that P|X ≡ 0. This quantitative estimate improves on previous work of Birch et al., who studied this problem from an algebraic viewpoint.
The topological method of proof presented here also allows us to obtain a partial solution to the Gromov-Milman problem (in
dimension two) on an isometric version of a theorem of Dvoretzky.
Received: 28 September 2004 |
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Keywords: | 46B20 |
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