Regular homotopy and total curvature II: sphere immersions into 3-space

被引：4

作者：

Ekholm, Tobias ^{[1
]}

机构：

[1] USC, Dept Math, Los Angeles, CA 90803 USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2006年 / 6卷

关键词：

D O I：

10.2140/agt.2006.6.493

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider properties of the total curvature functional on the space of 2-sphere immersions into 3-space. We show that the infimum over all sphere eversions of the maximum of the total curvature during an eversion is at most 8 pi and we establish a non-injectivity result for local minima.

引用

页码：493 / 512

页数：20

共 50 条

[1] Regular homotopy and total curvature I: circle immersions into surfaces
Ekholm, Tobias
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 : 459 - 492
[2] Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature II
Rossman, W
Umehara, M
Yamada, K
TOHOKU MATHEMATICAL JOURNAL, 2003, 55 (03) : 375 - 395
[3] ASSOCIATE HARMONIC IMMERSIONS IN 3-SPACE
MILNOR, TK
MICHIGAN MATHEMATICAL JOURNAL, 1990, 37 (02) : 179 - 190
[4] Regular homotopy classes of immersions of 3-manifolds into 5-space
Saeki, O
Szucs, A
Takase, M
MANUSCRIPTA MATHEMATICA, 2002, 108 (01) : 13 - 32
[5] Regular homotopy classes of immersions of 3-manifolds into 5-space
Osamu Saeki
András Szűcs
Masamichi Takase
manuscripta mathematica, 2002, 108 : 13 - 32
[6] THE STAR MEAN CURVATURE FLOW ON 3-SPHERE AND HYPERBOLIC 3-SPACE
Liu, Hsiao-Fan
ASIAN JOURNAL OF MATHEMATICS, 2020, 24 (03) : 483 - 500
[7] On bounds for total absolute curvature of surfaces in hyperbolic 3-space
Langevin, R
Solanes, G
COMPTES RENDUS MATHEMATIQUE, 2003, 336 (01) : 47 - 50
[8] Order one invariants of immersions of surfaces into 3-space
Tahl Nowik
Mathematische Annalen, 2004, 328 : 261 - 283
[9] Order one invariants of immersions of surfaces into 3-space
Nowik, T
MATHEMATISCHE ANNALEN, 2004, 328 (1-2) : 261 - 283
[10] HOMOTOPY GROUPS OF THE SPACE OF SELF MAPS OF THE PROJECTIVE 3-SPACE
Oshima, Katsumi
KODAI MATHEMATICAL JOURNAL, 2011, 34 (02) : 291 - 300

← 1 2 3 4 5 →