The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds

Eftekharinasab, Kaveh. "The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds." Communications in Mathematics 23.2 (2015): 101-112. <http://eudml.org/doc/276139>.

@article{Eftekharinasab2015,
abstract = {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 $\mathbb \{R\}$.},
author = {Eftekharinasab, Kaveh},
journal = {Communications in Mathematics},
keywords = {Fréchet manifolds; condition (CV); Finsler structures; Fredholm vector fields; Fréchet manifolds; condition (CV); Finsler structures; Fredholm vector fields},
language = {eng},
number = {2},
pages = {101-112},
publisher = {University of Ostrava},
title = {The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds},
url = {http://eudml.org/doc/276139},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Eftekharinasab, Kaveh
TI - The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds
JO - Communications in Mathematics
PY - 2015
PB - University of Ostrava
VL - 23
IS - 2
SP - 101
EP - 112
AB - 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 $\mathbb {R}$.
LA - eng
KW - Fréchet manifolds; condition (CV); Finsler structures; Fredholm vector fields; Fréchet manifolds; condition (CV); Finsler structures; Fredholm vector fields
UR - http://eudml.org/doc/276139
ER -