Existence proofs for rotationally symmetric translating solutions to mean curvature flow
Abstract
There exist rotationally symmetric translating solutions to mean curvature flow that can be written as a graph over Euclidean space. This result is well-known. Its proof uses the symmetry and techniques from partial differential equations. However, the result can also be formulated as an existence result for a singular ordinary differential equation. Here, we provide different methods to prove existence of these solutions based on the study of the singular ordinary differential equation without using methods from partial differential equations.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Differential Geometry and its Applications
- Publisher
- Elsevier BV
- Volume
- 102
- Pages
- 102327–102327
- Publication date
- 12 January 2026
- Language
- EN