Rotationally symmetric translating solitons of fully nonlinear extrinsic geometric flows: Classification and Applications

2025/12/29 by José Torres Santaella, Santaella, José Torres
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2512.23623

openalex publication_date 2025/12/29 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28

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.

Citations

• Classification of Semigraphical Translators
• Rotational symmetry of ancient solutions to fully nonlinear curvature flows
• A differential Harnack inequality for noncompact evolving hypersurfaces
• Ancient pancake solutions to fully nonlinear curvature flows
• Graphical Translators for Mean Curvature Flow
• On the existence of translating solutions of mean curvature flow in slab\n regions
• On the topology of translating solitons of the mean curvature flow
• Stability of translating solutions to mean curvature flow

Related

• Rotationally symmetric translating solutions to extrinsic geometric flows
• Maximum Principles and Consequences for γ-translators in ℝⁿ⁺¹ II
• Rotational symmetry of uniformly 3-convex translating solitons of mean curvature flow in higher dimensions
• Rotational symmetry of ancient solutions to fully nonlinear curvature flows
• Convexity and the Dirichlet problem of translating mean curvature flows