Abstract
A recent article (Li and Lv, J Geom Anal 30:417–447, 2020) considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in cases where the speed is a function of a degree-one homogeneous, concave and inverse concave function of the principle curvatures. In this article we consider self-similar solutions to these and related curvature flows that are not homogeneous in the principle curvatures, finding various situations where closed, convex curvature-pinched hypersurfaces contracting self-similarly are necessarily spheres.
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Acknowledgements
This research was supported by Discovery Grant DP180100431 of the Australian Research Council. Part of this work was completed while the author was at the Okinawa Institute of Science and Technology as part of the Visiting Mathematics Professors Program. The author is grateful for these sources of support.
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McCoy, J.A. Contracting Self-similar Solutions of Nonhomogeneous Curvature Flows. J Geom Anal 31, 6410–6426 (2021). https://doi.org/10.1007/s12220-020-00538-4
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DOI: https://doi.org/10.1007/s12220-020-00538-4