期刊
ARCHIV DER MATHEMATIK
卷 86, 期 6, 页码 561-568出版社
BIRKHAUSER VERLAG AG
DOI: 10.1007/s00013-006-1314-9
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Let k, n is an element of N, where n is odd. We show that there is an integer N = N( k, n) such that for every n-homogeneous polynomial P : R-N -> R there exists a linear subspace X -> R-N, dim X = k, such that P vertical bar(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.
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