Hausdorff measures and the Morse-Sard theorem

被引：0
|
作者：
Moreira, CGTD [1 ]
机构：
[1] IMPA, BR-22460320 Rio De Janeiro, Brazil
来源：
PUBLICACIONS MATEMATIQUES | 2001年 / 45卷 / 01期
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let F: U subset of R-n --> R-m be a differentiable junction and p < m an integer. If k greater than or equal to 1 is an integer, alpha epsilon [0,1] and F epsilon Ck+(alpha), if we set C-p(F) = {x epsilon U / rank(Df(x)) less than or equal to p} then the Hausdorff measure of dimension (p + n-p/k+alpha) of F(C-p(F)) is zero.
引用
收藏
页码：149 / 162
页数：14
相关论文
共 50 条
  • [31] On the Morse-Sard property and level sets of Sobolev and BV functions
    Bourgain, Jean
    Korobkov, Mikhail V.
    Kristensen, Jan
    REVISTA MATEMATICA IBEROAMERICANA, 2013, 29 (01) : 1 - 23
  • [32] Morse-Sard type results in sub-Riemannian geometry
    Rifford, L
    Trélat, E
    MATHEMATISCHE ANNALEN, 2005, 332 (01) : 145 - 159
  • [33] Morse-Sard type results in sub-Riemannian geometry
    L. Rifford
    E. Trélat
    Mathematische Annalen, 2005, 332 : 145 - 159
  • [34] The Trace Theorem, the Luzin N- and Morse-Sard Properties for the Sharp Case of Sobolev-Lorentz Mappings
    Korobkov, Mikhail V.
    Kristensen, Jan
    JOURNAL OF GEOMETRIC ANALYSIS, 2018, 28 (03) : 2834 - 2856
  • [35] Zygmund morse. Sard theorem
    Norton, Alec
    Journal of Geometric Analysis, 1994, 4 (03)
  • [36] On the Morse-Sard property and level sets of Wn, 1 Sobolev functions on Rn
    Bourgain, Jean
    Korobkov, Mikhail V.
    Kristensen, Jan
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2015, 700 : 93 - 112
  • [37] The curve selection lemma and the Morse–Sard theorem
    Carlos Gustavo Moreira
    Maria Aparecida Soares Ruas
    manuscripta mathematica, 2009, 129 : 401 - 408
  • [38] Approximate Morse-Sard type results for non-separable Banach spaces
    Azagra, D.
    Garcia-Bravo, M.
    Jimenez-Sevilla, M.
    JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 287 (04)
  • [39] The Morse criticality revisited and some new applications to the Morse–Sard theorem
    Xiaosong Kang
    Xu Xu
    Dunmu Zhang
    manuscripta mathematica, 2020, 161 : 467 - 485
  • [40] Some remarks about the Morse–Sard theorem and approximate differentiability
    Daniel Azagra
    Miguel García-Bravo
    Revista Matemática Complutense, 2020, 33 : 161 - 185
12345