Paper · Dec 29, 2025
Rotationally symmetric translating solitons of fully nonlinear extrinsic geometric flows: Classification and Applications
As on arXiv
Abstract
We develop a rotational theory for translating solitons of fully nonlinear extrinsic curvature flows in Euclidean space. Furthermore, we obtain fine asymptotic expansions for bowl-type translators in nondegenerate and degenerate regimes. On the other hand, we also introduce a signed-neck framework which yields the construction and classification of catenoidal-type translators, distinguishing complete embedded families from maximal admissible pieces according to the selected signed branch. As applications, we prove uniqueness results for strictly convex entire graphical translators with prescribed bowl-type asymptotics and obtain catenoidal-barrier nonexistence results for bounded graphical translators.
Comments: Comments are welcome!
Its neighbourhood
Connected papers
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.
-
Bowl Soliton Asymptotics and Applications
Topics Self-shrinkers & translators, Other curvature flows, Stability & uniqueness · Same author José Torres Santaella · Shared terms “bowl type”, “fully nonlinear”, “asymptotic expansions”
-
Rotationally symmetric translating solutions to extrinsic geometric flows
Topics Rotational symmetry & warped products, Self-shrinkers & translators, Other curvature flows · Shared terms “symmetric translating”, “extrinsic geometric”, “rotationally symmetric”
-
Maximum Principles and Consequences for -translators in
Topics Self-shrinkers & translators, Other curvature flows, Stability & uniqueness · Same author José Torres Santaella · Shared terms “extrinsic geometric”, “translating solitons”, “nonexistence”
-
A Bernstein problem for translating solutions to the mean curvature flow
Topics Rotational symmetry & warped products, Self-shrinkers & translators, Stability & uniqueness · Shared terms “graphical translators”, “entire graphical”, “translating solitons”
-
Rotational symmetry of ancient solutions to fully nonlinear curvature flows
Topics Rotational symmetry & warped products, Self-shrinkers & translators, Other curvature flows · Shared terms “fully nonlinear”, “symmetric translating”, “translating solitons”
-
Existence proofs for rotationally symmetric translating solutions to mean curvature flow
Topics Rotational symmetry & warped products, Self-shrinkers & translators · Shared terms “symmetric translating”, “rotationally symmetric”, “Euclidean space”
-
Translating solitons to higher order mean curvature flows in Riemannian products
Topics Rotational symmetry & warped products, Self-shrinkers & translators · Shared terms “translating solitons”, “bowl type”, “rotationally symmetric”
-
Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space
Topics Rotational symmetry & warped products, Self-shrinkers & translators, Stability & uniqueness · Shared terms “translating solitons”, “rotationally”, “graphical”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.