Ancient Solutions of Geometric Flows with Curvature Pinching

被引：13

作者：

Risa, Susanna ^{[1
]}

Sinestrari, Carlo ^{[2
]}

机构：

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

[2] Univ Roma Tor Vergata, Dipartimento Ingn Civile & Ingn Informat, Via Politecn 1, I-00133 Rome, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2019年 / 29卷 / 02期

关键词：

Ancient solutions; Mean curvature flow; Gauss curvature flow; Geometric flows; DEFORMING CONVEX HYPERSURFACES; POWERS; CLASSIFICATION; SINGULARITIES; SUBMANIFOLDS; CONTRACTION; ENTROPY; ROOT;

D O I：

10.1007/s12220-018-0036-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces.

引用

页码：1206 / 1232

页数：27

共 47 条

[1] Alessandroni R, 2010, ANN SCUOLA NORM-SCI, V9, P541
[2] HARNACK INEQUALITIES FOR EVOLVING HYPERSURFACES
ANDREWS, B
[J]. MATHEMATISCHE ZEITSCHRIFT, 1994, 217 (02) : 179 - 197
[3] CONTRACTION OF CONVEX HYPERSURFACES IN EUCLIDEAN-SPACE
ANDREWS, B
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (02) : 151 - 171
[4] Andrews B, 1996, J DIFFER GEOM, V43, P207
[5] Flow by powers of the Gauss curvature
Andrews, Ben
Guan, Pengfei
Ni, Lei
[J]. ADVANCES IN MATHEMATICS, 2016, 299 : 174 - 201
[6] Contracting convex hypersurfaces by curvature
Andrews, Ben
McCoy, James
Zheng, Yu
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2013, 47 (3-4) : 611 - 665
[7] Noncollapsing in mean-convex mean curvature flow
Andrews, Ben
[J]. GEOMETRY & TOPOLOGY, 2012, 16 (03) : 1413 - 1418
[8] CONVEX HYPERSURFACES WITH PINCHED PRINCIPAL CURVATURES AND FLOW OF CONVEX HYPERSURFACES BY HIGH POWERS OF CURVATURE
Andrews, Ben
McCoy, James
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (07) : 3427 - 3447
[9] Andrews B, 2010, J DIFFER GEOM, V85, P357
[10] Angenent S., 2015, ARXIV150301178

← 1 2 3 4 5 →