| Title:
|
New rotational integrals in space forms, with an application to surface area estimation (English) |
| Author:
|
Gual-Arnau, Ximo |
| Author:
|
Cruz-Orive, Luis M. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
489-501 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A surface area estimator for three-dimensional convex sets, based on the invariator principle of local stereology, has recently motivated its generalization by means of new rotational Crofton-type formulae using Morse theory. We follow a different route to obtain related formulae which are more manageable and valid for submanifolds in constant curvature spaces. As an application, we obtain a simplified version of the mentioned surface area estimator for non-convex sets of smooth boundary. (English) |
| Keyword:
|
critical point |
| Keyword:
|
height function |
| Keyword:
|
submanifold in space forms |
| Keyword:
|
invariator principle |
| Keyword:
|
local stereology |
| Keyword:
|
rotational formulae |
| Keyword:
|
surface area estimation |
| MSC:
|
53C65 |
| idZBL:
|
Zbl 06644008 |
| idMR:
|
MR3532255 |
| DOI:
|
10.1007/s10492-016-0143-9 |
| . |
| Date available:
|
2016-08-01T09:30:00Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145797 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
