Morse-Sard theorem for delta-convex curves

D. Pavlica

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 4, page 337-340
  • ISSN: 0862-7959

Abstract

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Let f : I → X be a delta-convex mapping, where I ⊂ ℝ is an open interval and X a Banach space. Let C f be the set of critical points of f . We prove that f ( C f ) has zero 1 / 2 -dimensional Hausdorff measure.

How to cite

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Pavlica, D.. "Morse-Sard theorem for delta-convex curves." Mathematica Bohemica 133.4 (2008): 337-340. <http://eudml.org/doc/250541>.

@article{Pavlica2008,
abstract = {Let $f\colon I\rightarrow X$ be a delta-convex mapping, where $I\subset \mathbb \{R\} $ is an open interval and $X$ a Banach space. Let $C_f$ be the set of critical points of $f$. We prove that $f(C_f)$ has zero $1/2$-dimensional Hausdorff measure.},
author = {Pavlica, D.},
journal = {Mathematica Bohemica},
keywords = {Morse-Sard theorem; delta-convex mapping; Morse-Sard theorem; delta-convex mapping},
language = {eng},
number = {4},
pages = {337-340},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Morse-Sard theorem for delta-convex curves},
url = {http://eudml.org/doc/250541},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Pavlica, D.
TI - Morse-Sard theorem for delta-convex curves
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 4
SP - 337
EP - 340
AB - Let $f\colon I\rightarrow X$ be a delta-convex mapping, where $I\subset \mathbb {R} $ is an open interval and $X$ a Banach space. Let $C_f$ be the set of critical points of $f$. We prove that $f(C_f)$ has zero $1/2$-dimensional Hausdorff measure.
LA - eng
KW - Morse-Sard theorem; delta-convex mapping; Morse-Sard theorem; delta-convex mapping
UR - http://eudml.org/doc/250541
ER -

References

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  1. Bourbaki, N., Éléments de mathématique IX., Les structures fondamentales de l'analyse. Livre IV: Fonctions d'une variable réelle (théorie élémentaire), Act. Sci. et Ind. vol. 1074, Hermann, Paris (1968). (1968) 
  2. Federer, H., Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer, New York (1969). (1969) Zbl0176.00801MR0257325
  3. Hartman, P., 10.2140/pjm.1959.9.707, Pacific J. Math. 9 (1959), 707-713. (1959) Zbl0093.06401MR0110773DOI10.2140/pjm.1959.9.707
  4. Kirchheim, B., 10.1090/S0002-9939-1994-1189747-7, Proc. Amer. Math. Soc. 121 (1994), 113-123. (1994) Zbl0806.28004MR1189747DOI10.1090/S0002-9939-1994-1189747-7
  5. Mattila, P., Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge Studies in Advanced Mathematics, 44, Cambridge University Press, Cambridge (1995). (1995) Zbl0819.28004MR1333890
  6. Pavlica, D., Zajíček, L., Morse-Sard theorem for d. c. functions and mappings on ℝ 2 , Indiana Univ. Math. J. 55 (2006), 1195-1207. (2006) MR2244604
  7. Veselý, L., Zajíček, L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. (Rozprawy Mat.) 289 (1989). (1989) MR1016045

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