Geodesic
On Tabachnikov's conjecture
Algebra i analiz, Tome 19 (2007) no. 1, pp. 177-193 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside aЁconvex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$.
Keywords: Geometric inequalities, mean absolute curvature, convexity. 
@article{AA_2007_19_1_a7,
     author = {A. I. Nazarov and F. V. Petrov},
     title = {On {Tabachnikov's} conjecture},
     journal = {Algebra i analiz},
     pages = {177--193},
     year = {2007},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2007_19_1_a7/}
}
TY  - JOUR
AU  - A. I. Nazarov
AU  - F. V. Petrov
TI  - On Tabachnikov's conjecture
JO  - Algebra i analiz
PY  - 2007
SP  - 177
EP  - 193
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AA_2007_19_1_a7/
LA  - ru
ID  - AA_2007_19_1_a7
ER  - 
%0 Journal Article
%A A. I. Nazarov
%A F. V. Petrov
%T On Tabachnikov's conjecture
%J Algebra i analiz
%D 2007
%P 177-193
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/AA_2007_19_1_a7/
%G ru
%F AA_2007_19_1_a7
A. I. Nazarov; F. V. Petrov. On Tabachnikov's conjecture. Algebra i analiz, Tome 19 (2007) no. 1, pp. 177-193. http://geodesic.mathdoc.fr/item/AA_2007_19_1_a7/

[1] Tabachnikov S., “The tale of a geometric inequality”, MASS Selecta, AMS, Providence, RI, 2003, 254–262 | MR

[2] Lagarias J., Richardson T., “Convexity and the average curvature of the plane curves”, Geom. Dedicata, 67 (1997), 1–38 | DOI | MR

[3] Aleksandrov A. D., Vnutrennyaya geometriya vypuklykh poverkhnostei, Gostekhizdat, M.-L., 1948

[4] http://mathworld.wolfram.com/SphericalTrigonometry.html

[5] http://mathworld.wolfram.com/Triangle.html

[6] http://mathworld.wolfram.com/SphericalExcess.html

[7] Zalgaller V. A., “O krivykh s ogranichennoi variatsiei povorota na vypukloi poverkhnosti”, Matem. sb., 26(68):2 (1950), 205–214 | MR | Zbl