Curvature evolution of nonconvex lens-shaped domains

被引：14

作者：

Bellettini, Giovanni ^{[1
,2
]}

Novaga, Matteo ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] INFN Lab Nazl Frascati, Rome, Italy

[3] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2011年 / 656卷

关键词：

CURVE SHORTENING FLOW; PARABOLIC EQUATIONS; MEAN-CURVATURE; PLANE-CURVES; MOTION; SINGULARITIES; SURFACES;

D O I：

10.1515/CRELLE.2011.041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point, as proved in [22]. Our theorem is the analog of the result of Grayson [13] for curvature flow of closed planar embedded curves.

引用

页码：17 / 46

页数：30

共 22 条

[11]

FREIRE A, ANAL PDE IN PRESS

[12]

GAGE M, 1986, J DIFFER GEOM, V23, P69

[13]

GRAYSON MA, 1987, J DIFFER GEOM, V26, P285

[14]

HAMILTON RS, 1986, J DIFFER GEOM, V24, P153

[15]

HATTENSCHWEILER J, 2007, THESIS ETH ZURICH

[16]

HUISKEN G, 1990, J DIFFER GEOM, V31, P285

[17]

Huisken G., 1998, ASIAN J MATH, V2, P127

[18]

ILMANEN T, 2009, COMMUNICATION

[19]

Mantegazza C, 2004, ANN SCUOLA NORM-SCI, V3, P235

[20] 2-DIMENSIONAL MOTION OF IDEALIZED GRAIN BOUNDARIES [J].

MULLINS, WW .

JOURNAL OF APPLIED PHYSICS, 1956, 27 (08) :900-904

← 1 2 3 →