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7. Behaviour of Variations under Polynomial Mappings

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1834)

Abstract

We study here the multidimensional variations of the image under a polynomial mapping of a semialgebraic set. We bound from above the i-th variation of the image by the i-th variation of the set and by the i-th Jacobian. This allows us to prove the quantitative Sard theorem for polynomial functions. We also define and study the “variations” of a polynomial mapping, and we finally bound from below the variation of the image.

Keywords

  • Polynomial Mapping
  • Volume Form
  • Geometric Measure Theory
  • Coarea Formula
  • Area Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Yosef Yomdin .

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© 2004 Springer-Verlag

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Yomdin, Y., Comte, G. (2004). 7. Behaviour of Variations under Polynomial Mappings. In: Tame Geometry with Application in Smooth Analysis. Lecture Notes in Mathematics, vol 1834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40960-1_7

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  • DOI: https://doi.org/10.1007/978-3-540-40960-1_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20612-5

  • Online ISBN: 978-3-540-40960-1

  • eBook Packages: Springer Book Archive