Local monotonicity of Hausdorff measures restricted to curves in n

Robert Černý

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 1, page 89-101
  • ISSN: 0010-2628

Abstract

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We give a sufficient condition for a curve γ : n to ensure that the 1 -dimensional Hausdorff measure restricted to γ is locally monotone.

How to cite

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Černý, Robert. "Local monotonicity of Hausdorff measures restricted to curves in $\mathbb {R}^n$." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 89-101. <http://eudml.org/doc/32483>.

@article{Černý2009,
abstract = {We give a sufficient condition for a curve $\gamma : \mathbb \{R\} \rightarrow \mathbb \{R\}^n$ to ensure that the $1$-dimensional Hausdorff measure restricted to $\gamma $ is locally monotone.},
author = {Černý, Robert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monotone measure; monotonicity formula; monotone measure; monotonicity formula},
language = {eng},
number = {1},
pages = {89-101},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Local monotonicity of Hausdorff measures restricted to curves in $\mathbb \{R\}^n$},
url = {http://eudml.org/doc/32483},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Černý, Robert
TI - Local monotonicity of Hausdorff measures restricted to curves in $\mathbb {R}^n$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 89
EP - 101
AB - We give a sufficient condition for a curve $\gamma : \mathbb {R} \rightarrow \mathbb {R}^n$ to ensure that the $1$-dimensional Hausdorff measure restricted to $\gamma $ is locally monotone.
LA - eng
KW - monotone measure; monotonicity formula; monotone measure; monotonicity formula
UR - http://eudml.org/doc/32483
ER -

References

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  1. Allard W.K., 10.2307/1970868, Ann. Math. 95 (1972), 417--491. (1972) Zbl0252.49028MR0307015DOI10.2307/1970868
  2. Černý R., Local monotonicity of measures supported by graphs of convex functions, Publ. Mat. 48 (2004), 369--380. (2004) Zbl1090.28004MR2091010
  3. Černý R., Local monotonicity of Hausdorff measures restricted to real analytic curves, submitted. 
  4. Kolář J., 10.1112/S0024609306018637, Bull. London Math. Soc. 38 (2006), 657--666. (2006) Zbl1115.49031MR2250758DOI10.1112/S0024609306018637
  5. Preiss D., 10.2307/1971410, Ann. Math. 125 (1987), 537--643. (1987) MR0890162DOI10.2307/1971410
  6. Simon L., Lectures on geometric measure theory, Proc. C.M.A., Australian National University, Vol. 3, 1983. Zbl0546.49019MR0756417

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