Local monotonicity of Hausdorff measures restricted to real analytic curves
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 1, page 37-56
- ISSN: 0010-2628
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topČerný, Robert. "Local monotonicity of Hausdorff measures restricted to real analytic curves." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 37-56. <http://eudml.org/doc/37745>.
@article{Černý2010,
abstract = {We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $\gamma : \mathbb \{R\} \rightarrow \mathbb \{R\}^N$, $N \ge 2$, is locally 1-monotone.},
author = {Černý, Robert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monotone measure; monotonicity formula; monotone measure; monotonicity formula},
language = {eng},
number = {1},
pages = {37-56},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Local monotonicity of Hausdorff measures restricted to real analytic curves},
url = {http://eudml.org/doc/37745},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Černý, Robert
TI - Local monotonicity of Hausdorff measures restricted to real analytic curves
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 37
EP - 56
AB - We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $\gamma : \mathbb {R} \rightarrow \mathbb {R}^N$, $N \ge 2$, is locally 1-monotone.
LA - eng
KW - monotone measure; monotonicity formula; monotone measure; monotonicity formula
UR - http://eudml.org/doc/37745
ER -
References
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- Černý R., Local monotonicity of Hausdorff measures restricted to curves in , Comment. Math. Univ. Carolin. 50 (2009), 89–101. MR2562806
- Kolář J., 10.1112/S0024609306018637, Bull. London Math. Soc. 38 (2006), 657–666. MR2250758DOI10.1112/S0024609306018637
- Preiss D., 10.2307/1971410, Ann. Math. 125 (1987), 537–643. MR0890162DOI10.2307/1971410
- Simon L., Lectures on Geometric Measure Theory, Proc. C.M.A., Australian National University Vol. 3, 1983. Zbl0546.49019MR0756417
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