Geodesic
Open map theorem for metric spaces
Algebra i analiz, Tome 17 (2005) no. 3, pp. 139-159 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An open map theorem for metric spaces is proved and some applications are discussed. The result on the existence of gradient flows of semiconcave functions is generalized to a large class of spaces.
Keywords: semi-convex functions, Aleksandrov spaces, differentials, gradient flow. 
@article{AA_2005_17_3_a7,
     author = {A. Lytchak},
     title = {Open map theorem for metric spaces},
     journal = {Algebra i analiz},
     pages = {139--159},
     year = {2005},
     volume = {17},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2005_17_3_a7/}
}
TY  - JOUR
AU  - A. Lytchak
TI  - Open map theorem for metric spaces
JO  - Algebra i analiz
PY  - 2005
SP  - 139
EP  - 159
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/AA_2005_17_3_a7/
LA  - en
ID  - AA_2005_17_3_a7
ER  - 
%0 Journal Article
%A A. Lytchak
%T Open map theorem for metric spaces
%J Algebra i analiz
%D 2005
%P 139-159
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/AA_2005_17_3_a7/
%G en
%F AA_2005_17_3_a7
A. Lytchak. Open map theorem for metric spaces. Algebra i analiz, Tome 17 (2005) no. 3, pp. 139-159. http://geodesic.mathdoc.fr/item/AA_2005_17_3_a7/

[BBI01] Burago D., Burago Yu., Ivanov S., A course in metric geometry, Grad. Stud. in Math., 33, Amer. Math. Soc., Providence, RI, 2001 | MR | Zbl

[BGP92] Burago Yu., Gromov M., Perelman G., “Prostranstva A. D. Aleksandrova s ogranichennymi snizu kriviznami”, Uspekhi mat. nauk, 47:2 (1992), 3–51 | MR | Zbl

[ВН99] Bridson M., Haefliger A., Metric spaces of non-positive curvature, Grundlehren Math. Wiss., 319, Springer-Verlag, Berlin, 1999 | MR | Zbl

[Fed70] Federer H., Geometric measure theory, Grundlehren Math. Wiss., 153, Springer-Verlag New York, Inc., New York, 1969 ; Nauka, M., 1987 | MR | Zbl | Zbl

[Kir94] Kirchheim B., “Rectifiable metric spaces: local structure and regularity of the Hausdorff measure”, Proc. Amer. Math. Soc., 121 (1994), 113–123 | DOI | MR | Zbl

[KM03] Kirchheim B., Magnani V., “A counterexample to metric differentiability”, Proc. Edinb. Math. Soc. (2), 46 (2003), 221–227 | MR | Zbl

[Lyta] Lytchak A., Almost convex subsets, Preprint, 2004 | MR | Zbl

[Lytb] Lytchak A., “Differentiation in metric spaces”, Algebra i analiz, 16:6 (2004), 128–161 | MR

[Nag02] Nagano K., “A volume convergence theorem for Alexandrov spaces with curvature bounded above”, Math. Z., 241 (2002), 127–163 | DOI | MR | Zbl

[Nik95] Nikolaev I., “The tangent cone of an Aleksandrov space of curvature $\le k$”, Manuscripta Math., 86 (1995), 137–147 | DOI | MR | Zbl

[Per94] Perelman G., “Nachala teorii Morsa na prostranstvakh Aleksandrova”, Algebra i analiz, 5:1 (1993), 232–241 | MR

[Pet99] Petrunin A., “Metric minimizing surfaces”, Electron. Res. Announc. Amer. Math. Soc., 5 (1999), 47–54 | DOI | MR | Zbl

[Pla02] Plaut C., “Metric spaces of curvature $\geq k$”, Handbook of Geometric Topology, North-Holland, Amsterdam, 2002, 819–898 | MR

[PP94] Perelman G., Petrunin A., Quasigeodesics and gradient curves in Alexandrov spaces, Preprint, 1994 | MR

[Res93] Reshetnyak Yu. G., “Dvumernye mnogoobraziya ogranichennoi krivizny”, Geometriya – 4. Neregulyarnaya rimanova geometriya, Itogi nauki i tekhn. Sovrem. probl. mat. Fundam. napravleniya, 70, VINITI, M., 1989, 7–189 | MR

[Sha77] Sharafutdinov V. A., “Teorema Pogorelova–Klingenberga dlya mnogoobrazii, gomeomorfnykh $R^n$”, Sib. mat. zh., 18:4 (1977), 915–925 | MR | Zbl