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Some Results on Space-Like Self-Shrinkers 被引量：3

Some Results on Space-Like Self-Shrinkers
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摘要 We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps. We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps.
作者 Hua Qiao LIU Yuan Long XIN
机构地区 School of Mathematics and Information Sciences Institute of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第1期69-82,共14页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China(Grant No.11271072) He’nan University Seed Fund
关键词 Space-like self-shrinker PSEUDO-DISTANCE volume growth RIGIDITY Space-like self-shrinker, pseudo-distance, volume growth, rigidity
分类号 O181 [理学—基础数学]
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参考文献22

  • 1Calabi, E.: Examples of Bernstein problems for some nonlinear equations. Proc. Syrup. Global Analysis U C. Berkeley, 1968.
  • 2Chau, A., Chen, J., Yuan, Y.: Rigidity of Entire self-shrinking solutions to curvature flows. J. Reine Angew. Math., 664, 229-239 (2012).
  • 3Chen, Q., Qiu, H. B.: Rigidity theorems for self-shrinker in Euclidean space and Pseudo-Eclideanspace, preprint Cheng, S. Y., Yau, S. T.: Maximal spacelike hypersurfaces in the LorentMinkowski spaces. Ann. Math., 104, 407 419 (1976).
  • 4Cheng, X., Zhou, D. T.: Volume estimates about shrinkers, arXiv:l106.4950.
  • 5Colding, T. H., Minicozzi II, W. P.: Generic mean curvature flow I; generic singularities. Ann. Math., 175, 755433 (2012).
  • 6Ding, Q., Wang, Z. Z.: On the self-shrinking system in arbitrary codimensional spaces, arXiv:1012.0429v2 (math.DG].
  • 7Ding, Q., Xin, Y. L., Volume growth, eigenvalue and compactness for self-shrinkers. Asian J. Math., 17, 443-456 (2013).
  • 8Ding, Q., Xin, Y. L.: The rigidity theorems for Lagrangian self-shrinkers. J. Reine Angew. Math., accepted, arXiv:l l12.2453 [math.DG1.
  • 9Ding, Q., Xin, Y. L.: The rigidity theorems for Lagrangian self-shrinkers. J. Reine Angew. Math., accepted, arXiv:l 112.2453 [math.DG].
  • 10Ecker, K.: On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetime. J. Austral. Math. Soe. Set. A, 55(1), 41-59 (1993).

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Acta Mathematica Sinica,English Series
2016年 第1期

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