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A bridge between Dubovitskiĭ-Federer theorems and the coarea formula

Abstract:

The Morse-Sard theorem requires that a mapping v : ℝn → ℝm is of class Ck, k > max(n - m, 0). In 1957 Dubovitskiĭ generalized this result by proving that almost all level sets for a Ck mapping has Hs-negligible intersection with its critical set, where s = max(n - m - k + 1, 0). Here the critical set, or m-critical set is defined as Zv,m = {x ∈ ℝn : rank ∇v(x) < m}. Another generalization was obtained independently by Dubovitskiĭ and Federer in 1966, namely for Ck mappings v : ℝn → ℝ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1016/j.jfa.2016.10.031

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Department:
Oxford, MPLS, Mathematical Institute
Hajlasz, P More by this author
Korobkov, MV More by this author
Publisher:
Elsevier Publisher's website
Journal:
Journal of Functional Analysis Journal website
Volume:
272
Issue:
3
Pages:
1265–1295
Publication date:
2016-11-05
Acceptance date:
2016-11-01
DOI:
ISSN:
1096-0783
Pubs id:
pubs:656461
URN:
uri:4bae78bd-f3c0-4fd0-b22e-f6232f43d374
UUID:
uuid:4bae78bd-f3c0-4fd0-b22e-f6232f43d374
Local pid:
pubs:656461

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