Abstract
In this chapter we briefly describe some further applications of the results and methods developed in the preceeding chapters.
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10.1 Applications of Quantitative Sard and Transversality Theorems
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10.1.1 Maxima of smooth families
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10.1.2 Average topological complexity of fibers
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10.1.3 Quantitative Kupka-Smale Theorem
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10.1.4 Possible Applications in Numerical Analysis
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10.2 Semialgebraic Complexity of Functions
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10.2.1 Semialgebraic Complexity
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10.2.2 Semialgebraic Complexity and Sard Theorem
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10.2.3 Complexity of Functions on Infinite-Dimensional Spaces
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10.3 Additional Directions
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10.3.1 Asymptotic Critical Values of Semialgebraic and Tame Mappings
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10.3.2 Morse-Sard Theorem in Sobolev Spaces
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10.3.3 From Global to Local: Real Equisingularity
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10.3.4 \(\mathcal{C}^k\) Reparametrization of Semialgebraic Sets
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10.3.5 Bernstein-Type Inequalities for Algebraic Functions
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10.3.6 Polynomial Control Problems
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10.3.7 Quantitative Singularity Theory
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© 2004 Springer-Verlag
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Yomdin, Y., Comte, G. (2004). 10. Some Applications and Related Topics. 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_10
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DOI: https://doi.org/10.1007/978-3-540-40960-1_10
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20612-5
Online ISBN: 978-3-540-40960-1
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