Geodesic
Regular homotopy and total curvature I: circle immersions into surfaces
Ekholm, Tobias1
1Department of mathematics, USC, Los Angeles CA 90803, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 459-492
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima.

DOI : 10.2140/agt.2006.6.459
Keywords: circle immersion, geodesic curvature, regular curve, regular homotopy, Riemann surface, total curvature

Ekholm, Tobias  1

1 Department of mathematics, USC, Los Angeles CA 90803, USA 
@article{10_2140_agt_2006_6_459,
     author = {Ekholm, Tobias},
     title = {Regular homotopy and total curvature {I:} circle immersions into surfaces},
     journal = {Algebraic and Geometric Topology},
     pages = {459--492},
     year = {2006},
     volume = {6},
     number = {1},
     doi = {10.2140/agt.2006.6.459},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.459/}
}
TY  - JOUR
AU  - Ekholm, Tobias
TI  - Regular homotopy and total curvature I: circle immersions into surfaces
JO  - Algebraic and Geometric Topology
PY  - 2006
SP  - 459
EP  - 492
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.459/
DO  - 10.2140/agt.2006.6.459
ID  - 10_2140_agt_2006_6_459
ER  - 
%0 Journal Article
%A Ekholm, Tobias
%T Regular homotopy and total curvature I: circle immersions into surfaces
%J Algebraic and Geometric Topology
%D 2006
%P 459-492
%V 6
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.459/
%R 10.2140/agt.2006.6.459
%F 10_2140_agt_2006_6_459
Ekholm, Tobias. Regular homotopy and total curvature I: circle immersions into surfaces. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 459-492. doi: 10.2140/agt.2006.6.459

[1] V I Arnol’D, Plane curves, their invariants, perestroikas and classifications, from: "Singularities and bifurcations", Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 33

[2] T Ekholm, Regular homotopy and total curvature II: sphere immersions into $3$-space, Algebr. Geom. Topol. 6 (2006) 493

[3] M Gromov, Partial differential relations, Ergebnisse series 9, Springer (1986)

[4] M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242

[5] A V Inshakov, Invariants of types $j^+, j^-$ and $\mathrm st$ of smooth curves on two-dimensional manifolds, Funktsional. Anal. i Prilozhen. 33 (1999) 35, 96

[6] J Jost, Riemannian geometry and geometric analysis, Universitext, Springer (1998)

[7] L A Lyusternik, A I Fet, Variational problems on closed manifolds, Doklady Akad. Nauk SSSR $($N.S.$)$ 81 (1951) 17

[8] S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. $(2)$ 69 (1959) 327

[9] V Tchernov, Arnold-type invariants of wave fronts on surfaces, Topology 41 (2002) 1

Cité par Sources :