| Title:
|
Curves in Banach spaces which allow a $C^{1,\rm BV}$ parametrization or a parametrization with finite convexity (English) |
| Author:
|
Duda, Jakub |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
1057-1085 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a complete characterization of those $f\colon [0,1] \to X$ (where $X$ is a Banach space) which allow an equivalent $C^{1,\rm BV}$ parametrization (i.e., a $C^1$ parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for $X= \mathbb R^n$. We present examples which show applicability of our characterizations. For example, we show that the $C^{1,\rm BV}$ and $C^2$ parametrization problems are equivalent for $X=\mathbb R$ but are not equivalent for $X = \mathbb R^2$. (English) |
| Keyword:
|
curve in Banach spaces |
| Keyword:
|
$C^{1,\rm BV}$ parametrization |
| Keyword:
|
parametrization with bounded convexity |
| MSC:
|
26A51 |
| MSC:
|
26E20 |
| MSC:
|
53A04 |
| idZBL:
|
Zbl 06373962 |
| idMR:
|
MR3165515 |
| DOI:
|
10.1007/s10587-013-0072-7 |
| . |
| Date available:
|
2014-01-28T14:18:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143617 |
| . |
| Reference:
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