The H-flow translating solitons in R^3 and R^4

Abstract

Motivated by Ilmanen's correspondence, we present an explicit solution to the prescribed Hoffman-Osserman Gauss map problem for non-minimal translators to the mean curvature flow in Euclidean 4-space. We propose a conjecture on the non-existence of Jenkins-Serrin type unit-speed graphical translators.

Example 3 and an acknowledgement are added. As an application of our prescribed Gauss map representation of translators in R^4, we explicitly determine the Hoffman-Osserman Gauss map of the Hamiltonian stationary Lagrangian translator in C^2

References in corpus (5)

• Subsequent Singularities in Mean-Convex Mean Curvature Flow
• Minimal surfaces and mean curvature flow
• Translating solutions to Lagrangian mean curvature flow
• Some examples of self-similar solutions and translating solitons for mean curvature flow
• Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane