| Title:
|
Local monotonicity of Hausdorff measures restricted to real analytic curves (English) |
| Author:
|
Černý, Robert |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
37-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $\gamma: \mathbb R \to \mathbb R^N$, $N \ge 2$, is locally 1-monotone. (English) |
| Keyword:
|
monotone measure |
| Keyword:
|
monotonicity formula |
| MSC:
|
28A75 |
| MSC:
|
49Q15 |
| MSC:
|
53A10 |
| idZBL:
|
Zbl 1224.53016 |
| idMR:
|
MR2666079 |
| . |
| Date available:
|
2010-05-21T12:31:47Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140087 |
| . |
| Reference:
|
[1] Černý R.: Local monotonicity of measures supported by graphs of convex functions.Publ. Mat. 48 (2004), 369–380. MR 2091010 |
| Reference:
|
[2] Černý R.: Local monotonicity of Hausdorff measures restricted to curves in $\mathbb R^n$.Comment. Math. Univ. Carolin. 50 (2009), 89–101. MR 2562806 |
| Reference:
|
[3] Kolář J.: Non-regular tangential behavior of a monotone measure.Bull. London Math. Soc. 38 (2006), 657–666. MR 2250758, 10.1112/S0024609306018637 |
| Reference:
|
[4] Preiss D.: Geometry of measures in $\mathbb R^n$: Distribution, rectifiability and densities.Ann. Math. 125 (1987), 537–643. MR 0890162, 10.2307/1971410 |
| Reference:
|
[5] Simon L.: Lectures on Geometric Measure Theory.Proc. C.M.A., Australian National University Vol. 3, 1983. Zbl 0546.49019, MR 0756417 |
| . |
