| Title:
|
The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds (English) |
| Author:
|
Eftekharinasab, Kaveh |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
23 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
101-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study Lipschitz-Fredholm vector fields on bounded Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded Fréchet-Finsler manifold endowed with a connection $\mathcal {K}$ and if $\xi$ is a smooth Lipschitz-Fredholm vector field on $M$ with respect to $\mathcal {K}$ which satisfies condition (WCV), then, for any smooth functional $l$ on $M$ which is associated to $\xi$, the set of the critical values of $l$ is of first category in $\mathbb{R}$. Therefore, the set of the regular values of $l$ is a residual Baire subset of $\mathbb {R}$. (English) |
| Keyword:
|
Fréchet manifolds |
| Keyword:
|
condition (CV) |
| Keyword:
|
Finsler structures |
| Keyword:
|
Fredholm vector fields |
| MSC:
|
58B15 |
| MSC:
|
58B20 |
| MSC:
|
58K05 |
| idZBL:
|
Zbl 1338.58027 |
| idMR:
|
MR3436678 |
| . |
| Date available:
|
2016-01-19T13:46:11Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144798 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
