Gauss curvature flow: the fate of the rolling stones

被引:219
作者
Andrews, B [1 ]
机构
[1] Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia
关键词
D O I
10.1007/s002220050344
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove Firey's 1974 conjecture that convex surfaces moving by their Gauss curvature become spherical as they contract to points.
引用
收藏
页码:151 / 161
页数:11
相关论文
共 14 条
[2]  
ANDREWS B, 1998, 00998 MRR AUSTR NAT
[3]  
CHOU K, 1985, COMMUN PUR APPL MATH, V38, P867
[4]  
CHOW B, 1985, J DIFFER GEOM, V22, P117
[5]   ON HARNACK INEQUALITY AND ENTROPY FOR THE GAUSSIAN CURVATURE FLOW [J].
CHOW, B .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (04) :469-483
[6]   SHAPES OF WORN STONES [J].
FIREY, WJ .
MATHEMATIKA, 1974, 21 (41) :1-11
[7]  
Hamilton R., 1994, DISCOURSES MATH APPL, V3, P69
[8]  
Hamilton R., 1994, COMMUN ANAL GEOM, V2, P155
[9]  
HAMILTON RS, 1986, J DIFFER GEOM, V24, P153
[10]   Self-similar solutions for the Gauss curvature evolution of rotationally symmetric surfaces [J].
Ishimura, N .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 33 (01) :97-104