| Title:
|
Local monotonicity of Hausdorff measures restricted to curves in $\Bbb R^n$ (English) |
| Author:
|
Černý, Robert |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
89-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a sufficient condition for a curve $\gamma: \Bbb R \to \Bbb R^n$ to ensure that the $1$-dimensional Hausdorff measure restricted to $\gamma$ is locally monotone. (English) |
| Keyword:
|
monotone measure |
| Keyword:
|
monotonicity formula |
| MSC:
|
28A75 |
| MSC:
|
49Q15 |
| MSC:
|
53A10 |
| idZBL:
|
Zbl 1212.53006 |
| idMR:
|
MR2562806 |
| . |
| Date available:
|
2009-08-18T12:23:19Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133417 |
| . |
| Reference:
|
[1] Allard W.K.: On the first variation of a varifold.Ann. Math. 95 (1972), 417--491. Zbl 0252.49028, MR 0307015, 10.2307/1970868 |
| Reference:
|
[2] Černý R.: Local monotonicity of measures supported by graphs of convex functions.Publ. Mat. 48 (2004), 369--380. Zbl 1090.28004, MR 2091010 |
| Reference:
|
[3] Černý R.: Local monotonicity of Hausdorff measures restricted to real analytic curves.submitted. |
| Reference:
|
[4] Kolář J.: Non-regular tangential behaviour of a monotone measure.Bull. London Math. Soc. 38 (2006), 657--666. Zbl 1115.49031, MR 2250758, 10.1112/S0024609306018637 |
| Reference:
|
[5] Preiss D.: Geometry of measures in $\Bbb R^n$: Distribution, rectifiability and densities.Ann. Math. 125 (1987), 537--643. MR 0890162, 10.2307/1971410 |
| Reference:
|
[6] Simon L.: Lectures on geometric measure theory.Proc. C.M.A., Australian National University, Vol. 3, 1983. Zbl 0546.49019, MR 0756417 |
| . |
