Abstract
We study space-like self-shrinkers of dimension n in pseudo-Euclidean space R m+n m 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.
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Supported by National Natural Science Foundation of China (Grant No. 11271072) and He’nan University Seed Fund
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Liu, H.Q., Xin, Y.L. Some results on space-like self-shrinkers. Acta. Math. Sin.-English Ser. 32, 69–82 (2016). https://doi.org/10.1007/s10114-014-4082-7
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DOI: https://doi.org/10.1007/s10114-014-4082-7