Abstract
In this paper, we study the inverse anisotropic curvature flow from strictly convex hypersurfaces. We show the long-time existence and the convergence to the Wulff shape after rescaling, under certain conditions on the general speed functions.
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Acknowledgements
Part of this work has been done when I was a postdoc supported by CRC Postdoc Fellowship at the Department of Mathematics and Statistics, McGill University. I would like to thank the department for its hospitality. I appreciate Professors Bo Guan, Pengfei Guan, Guofang Wang and Zhizhang Wang for many stimulating discussions and suggestions on this subject. In the first version of this paper, we have only showed the convergence result for special case \(f=\left( \frac{\sigma _n}{\sigma _{n-k}}\right) ^{\frac{1}{k}}\). I am indebted to Professor Ben Andrews who suggests me a simpler argument which yields improvement of the result in this present version. Research of CX is supported in part by NSFC (Grant No. 11501480) and the Fundamental Research Funds for the Central Universities (Grant No. 20720150012).
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Xia, C. Inverse Anisotropic Curvature Flow from Convex Hypersurfaces. J Geom Anal 27, 2131–2154 (2017). https://doi.org/10.1007/s12220-016-9755-2
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DOI: https://doi.org/10.1007/s12220-016-9755-2