Abstract
This paper mainly considers the translating soliton of H k-flow for k > 0. We give the asymptotic expression of the entire rotationally symmetric translating soliton, and obtain non-convex “Wing-like” solution as well as two barrier solutions. Moreover, we show that the solution with polynomial growth keeps its growth rate when evolution.
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Clutterbuck J, Schnürer O C, Schulze F. Stability of translating solutions to mean curvature flow. Calc Var Partal Differ Egn, 2007, 29: 281–293
Schulze F. Evolution of convex hypersurfaces by powers of mean curvature. Math Z, 2005, 251: 721–733
Sheng W M, Wu C. On asymptotic behavior for singularities of the powers of mean curvature flow. Chin Ann Math Ser B, 2009, 30: 51–66
Urbas J. Complete noncompact self-similar solutions of Gauss curvature flows I. Positive powers. Math Ann, 1998, 311: 251–274
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Sheng, W., Wu, C. Rotationally symmetric translating soliton of H k-flow. Sci. China Math. 53, 1011–1016 (2010). https://doi.org/10.1007/s11425-010-0050-6
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DOI: https://doi.org/10.1007/s11425-010-0050-6