As on arXiv
Abstract
In this paper, we obtain the asymptotic expansion for the analogue of the bowl-soliton for a large `nondegenerate' class of fully nonlinear curvature flows. We use this to show the uniqueness of these bowl-type solitons in their asymptotic class. We also give examples to illustrate the situation for `degenerate' speeds and how they different they can be. Finally, we show how to construct `wing-like' solitons for these flows, which are complete, connected translators that are not graphical, entire or convex. We also obtain asymptotic expansions for them to show the variety of solutions that one can obtain depending on the choice of speed function.
Comments: 6 figures
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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Rotationally symmetric translating solitons of fully nonlinear extrinsic geometric flows: Classification and Applications
Topics Self-shrinkers & translators, Other curvature flows, Stability & uniqueness · Same author José Torres Santaella · Shared terms “bowl type”, “fully nonlinear”, “asymptotic expansions”
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Maximum Principles and Consequences for -translators in
Topics Self-shrinkers & translators, Other curvature flows, Stability & uniqueness · Same author José Torres Santaella
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Translators to Higher Order Mean Curvature Flows in and
Topics Self-shrinkers & translators, Stability & uniqueness · Shared terms “bowl soliton”, “bowl type”
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Ancient pancake solutions to fully nonlinear curvature flows
Topics Other curvature flows · Same author Sathya Rengaswami · Shared terms “nonlinear curvature”, “fully nonlinear”
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Rotationally symmetric translating solutions to extrinsic geometric flows
Topics Self-shrinkers & translators, Other curvature flows · Shared terms “bowl soliton”, “speed function”, “asymptotics”
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A Bernstein problem for translating solutions to the mean curvature flow
Topics Self-shrinkers & translators, Stability & uniqueness · Shared terms “bowl soliton”, “graphical”
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Rigidity results for mean curvature flow graphical translators moving in non-graphical direction
Topics Self-shrinkers & translators, Stability & uniqueness · Shared terms “graphical”
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Rotational symmetry of ancient solutions to fully nonlinear curvature flows
Topics Self-shrinkers & translators, Other curvature flows · Shared terms “nonlinear curvature”, “fully nonlinear”
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