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- W4224257557 abstract "In this paper we construct complete convex hypersurfaces in $mathbb R^{n+1}$ which translate under the flow by powers $alpha in (0, frac1{n+2})$ of the Gauss curvature. The level set of each solution is asymptotic to a shrinking soliton for the flow by power $frac alpha {1-alpha}$ of the Gauss curvature in $mathbb R^n$. For example, our construction reveals the existence of translators whose level set converges to the sphere, simplex, hypercube and so on. The translating solitons exist as a family whose parameters correspond to Jacobi fields, solutions to linearized equation around the asymptotic profile." @default.
- W4224257557 created "2022-04-26" @default.
- W4224257557 creator A5084168318 @default.
- W4224257557 date "2022-04-19" @default.
- W4224257557 modified "2023-09-26" @default.
- W4224257557 title "On existence of hypersurfaces translating by powers of Gauss curvature" @default.
- W4224257557 doi "https://doi.org/10.48550/arxiv.2204.09002" @default.
- W4224257557 hasPublicationYear "2022" @default.
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